Celebratio Mathematica

J. Hyam Rubinstein

Topology

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J. H. Ru­bin­stein: “Min­im­al prime ideals and com­pac­ti­fic­a­tions,” J. Aust. Math. Soc. 13 (1972), pp. 423–​432. MR 0417007 Zbl 0263.​06010 article

J. H. Ru­bin­stein: Iso­top­ies of in­com­press­ible sur­faces in three di­men­sion­al man­i­folds. Ph.D. thesis, Uni­versity of Cali­for­nia, Berke­ley, 1974. Ad­vised by J. R. Stallings, Jr. MR 2940549 phdthesis

J. H. Ru­bin­stein: “Hee­gaard split­tings and a the­or­em of Livesay,” Proc. Am. Math. Soc. 60 (1976), pp. 317–​320. MR 0420625 Zbl 0314.​57002 article

J. H. Ru­bin­stein: “Iso­top­ies of the pro­ject­ive plane in 3-man­i­folds,” To­po­logy 16 : 3 (1977), pp. 217–​226. MR 0478165 Zbl 0363.​57003 article

J. H. Ru­bin­stein: “One-sided Hee­gaard split­tings of 3-man­i­folds,” Pac. J. Math. 76 : 1 (1978), pp. 185–​200. MR 0488064 Zbl 0394.​57013 article

J. H. Ru­bin­stein and C. Gardiner: “A note on a 3-di­men­sion­al ho­mo­gen­eous space,” Com­pos. Math. 39 : 3 (1979), pp. 297–​299. MR 550645 Zbl 0413.​57008 article

J. H. Ru­bin­stein: “Free ac­tions of some fi­nite groups on \( \mathbb{S}^{3} \), I,” Math. Ann. 240 : 2 (1979), pp. 165–​175. MR 524664 Zbl 0382.​57019 article

J. H. Ru­bin­stein: “On 3-man­i­folds that have fi­nite fun­da­ment­al group and con­tain Klein bottles,” Trans. Am. Math. Soc. 251 (July 1979), pp. 129–​137. MR 531972 Zbl 0414.​57005 article

J. H. Ru­bin­stein: “Dehn’s lemma and handle de­com­pos­i­tions of some 4-man­i­folds,” Pac. J. Math. 86 : 2 (1980), pp. 565–​569. MR 590570 Zbl 0446.​57025 article

J. H. Ru­bin­stein: “Nonori­ent­able sur­faces in some non-Haken 3-man­i­folds,” Trans. Am. Math. Soc. 270 : 2 (April 1982), pp. 503–​524. MR 645327 Zbl 0496.​57004 article

M. Cull­er, W. Jaco, and H. Ru­bin­stein: “In­com­press­ible sur­faces in once-punc­tured tor­us bundles,” Proc. Lon­don Math. Soc. (3) 45 : 3 (1982), pp. 385–​419. MR 675414 Zbl 0515.​57002 article

J. H. Ru­bin­stein and J. S. Birman: “One-sided Hee­gaard split­tings and homeotopy groups of some 3-man­i­folds,” Proc. Lond. Math. Soc. (3) 49 : 3 (1984), pp. 517–​536. MR 759302 Zbl 0527.​57003 article

I. R. Aitchis­on and J. H. Ru­bin­stein: “Fibered knots and in­vol­u­tions on ho­mo­topy spheres,” pp. 1–​74 in Four-man­i­fold the­ory (Durham, NH, 4–10 Ju­ly 1982). Edi­ted by C. Gor­don and R. Kirby. Con­tem­por­ary Math­em­at­ics 35. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1984. MR 780575 Zbl 0567.​57015 incollection

J. H. Ru­bin­stein: “Em­bed­ded min­im­al sur­faces in 3-man­i­folds with pos­it­ive scal­ar curvature,” Proc. Am. Math. Soc. 95 : 3 (November 1985), pp. 458–​462. MR 806087 Zbl 0584.​53004 article

W. Van­nini and J. H. Ru­bin­stein: “Sym­met­ric cut loci in Rieman­ni­an man­i­folds,” Proc. Am. Math. Soc. 94 : 2 (1985), pp. 317–​320. MR 784185 Zbl 0563.​53037 article

C. Hodg­son and J. H. Ru­bin­stein: “In­vol­u­tions and iso­top­ies of lens spaces,” pp. 60–​96 in Knot the­ory and man­i­folds (Van­couver, BC, 2–4 June 1983). Edi­ted by D. Rolf­sen. Lec­ture Notes in Math­em­at­ics 1144. Spring­er (Ber­lin), 1985. MR 823282 Zbl 0605.​57022 incollection

J. T. Pitts and J. H. Ru­bin­stein: “Ex­ist­ence of min­im­al sur­faces of bounded to­po­lo­gic­al type in three-man­i­folds,” pp. 163–​176 in Minicon­fer­ence on geo­metry and par­tial dif­fer­en­tial equa­tions (Can­berra, 1–3 Au­gust 1985). Edi­ted by L. M. Si­mon and N. S. Trudinger. Pro­ceed­ings of the Centre for Math­em­at­ic­al Ana­lys­is, Aus­trali­an Na­tion­al Uni­versity 10. Aus­trali­an Na­tion­al Uni­versity (Can­berra), 1986. First minicon­fer­ence. MR 857665 Zbl 0602.​49028 incollection

J. Hass and J. H. Ru­bin­stein: “One-sided closed geodesics on sur­faces,” Mich. Math. J. 33 : 2 (1986), pp. 155–​168. MR 837574 Zbl 0614.​53035 article

P. R. A. Leviton and J. H. Ru­bin­stein: “De­form­ing Rieman­ni­an met­rics on the 2-sphere,” pp. 123–​127 in Minicon­fer­ence on geo­metry and par­tial dif­fer­en­tial equa­tions (Can­berra, 1–3 Au­gust 1985). Edi­ted by L. M. Si­mon and N. S. Trudinger. Pro­ceed­ings of the Centre for Math­em­at­ic­al Ana­lys­is, Aus­trali­an Na­tion­al Uni­versity 10. Aus­trali­an Na­tion­al Uni­versity (Can­berra), 1986. First minicon­fer­ence. MR 857659 Zbl 0619.​53025 incollection

W. Jaco and J. H. Ru­bin­stein: “A piece­wise lin­ear the­ory of min­im­al sur­faces in 3-man­i­folds,” pp. 99–​110 in Minicon­fer­ence on geo­metry and par­tial dif­fer­en­tial equa­tions (Can­berra, 1–3 Au­gust 1985). Edi­ted by L. M. Si­mon and N. S. Trudinger. Pro­ceed­ings of the Centre for Math­em­at­ic­al Ana­lys­is, Aus­trali­an Na­tion­al Uni­versity 10. Aus­trali­an Na­tion­al Uni­versity (Can­berra), 1986. First minicon­fer­ence. MR 857657 Zbl 0596.​53007 incollection

P. R. A. Leviton and J. H. Ru­bin­stein: “De­form­ing Rieman­ni­an met­rics on com­plex pro­ject­ive spaces,” pp. 86–​95 in Minicon­fer­ence on geo­metry and par­tial dif­fer­en­tial equa­tions (Can­berra, 26–27 Au­gust 1986). Edi­ted by J. E. Hutchin­son and L. M. Si­mon. Pro­ceed­ings of the Centre for Math­em­at­ic­al Ana­lys­is, Aus­trali­an Na­tion­al Uni­versity 12. Aus­trali­an Na­tion­al Uni­versity (Can­berra), 1987. Second minicon­fer­ence. MR 924430 Zbl 0642.​53074 incollection

J. T. Pitts and J. H. Ru­bin­stein: “Ap­plic­a­tions of min­im­ax to min­im­al sur­faces and the to­po­logy of 3-man­i­folds,” pp. 137–​170 in Minicon­fer­ence on geo­metry and par­tial dif­fer­en­tial equa­tions (Can­berra, 26–27 Au­gust 1986). Edi­ted by J. E. Hutchin­son and L. M. Si­mon. Pro­ceed­ings of the Centre for Math­em­at­ic­al Ana­lys­is, Aus­trali­an Na­tion­al Uni­versity 12. Aus­trali­an Na­tion­al Uni­versity (Can­berra), 1987. Second minicon­fer­ence. MR 924434 Zbl 0639.​49030 incollection

J. Hass, H. Ru­bin­stein, and P. Scott: “Cov­er­ing spaces of 3-man­i­folds,” Bull. Am. Math. Soc., New Ser. 16 : 1 (January 1987), pp. 117–​119. MR 866028 Zbl 0624.​57016 article

J. T. Pitts and J. H. Ru­bin­stein: “Equivari­ant min­im­ax and min­im­al sur­faces in geo­met­ric three-man­i­folds,” Bull. Am. Math. Soc., New Ser. 19 : 1 (1988), pp. 303–​309. MR 940493 Zbl 0665.​49034 article

W. Jaco and J. H. Ru­bin­stein: “PL min­im­al sur­faces in 3-man­i­folds,” J. Dif­fer. Geom. 27 : 3 (1988), pp. 493–​524. MR 940116 Zbl 0652.​57005 article

J. H. Ru­bin­stein and D. Thomas: The Stein­er prob­lem of shortest net­works, 1988. From un­pub­lished pro­ceed­ings of the third Aus­trali­an tele­traffic re­search sem­in­ar (Mel­bourne, Novem­ber 1988). misc

I. R. Aitchis­on and J. H. Ru­bin­stein: “Heav­en & hell,” pp. 5–​24 in Pro­ceed­ings of the sixth in­ter­na­tion­al col­loqui­um on dif­fer­en­tial geo­metry (San­ti­ago de Com­postela, Spain, 19–23 Septem­ber 1988). Edi­ted by L. A. Cor­d­ero. Cursos e Con­gresos da Uni­ver­sid­ade de San­ti­ago de Com­postela 61. Uni­ver­sid­ad San­ti­ago de Com­postela, 1989. MR 1040833 Zbl 0737.​57004 incollection

J. Hass, H. Ru­bin­stein, and P. Scott: “Com­pac­ti­fy­ing cov­er­ings of closed 3-man­i­folds,” J. Dif­fer. Geom. 30 : 3 (1989), pp. 817–​832. MR 1021374 Zbl 0693.​57011 article

J. H. Ru­bin­stein and D. Thomas: Min­im­al cost net­works in the plane, 1989. From un­pub­lished pro­ceed­ings of the fourth Aus­trali­an tele­traffic re­search sem­in­ar (Bond Uni­versity, Ro­bina, Aus­tralia, Decem­ber 1989). misc

W. Jaco and J. H. Ru­bin­stein: “PL equivari­ant sur­gery and in­vari­ant de­com­pos­i­tions of 3-man­i­folds,” Adv. in Math. 73 : 2 (1989), pp. 149–​191. MR 987273 Zbl 0682.​57005 article

J. H. Ru­bin­stein and G. A. Swarup: “On Scott’s core the­or­em,” Bull. Lond. Math. Soc. 22 : 5 (1990), pp. 495–​498. MR 1082023 Zbl 0709.​57012 article

I. R. Aitchis­on and J. H. Ru­bin­stein: “An in­tro­duc­tion to poly­hed­ral met­rics of non­posit­ive curvature on 3-man­i­folds,” pp. 127–​161 in Geo­metry of low-di­men­sion­al man­i­folds (Durham, UK, Ju­ly 1989), vol. 2: Sym­plect­ic man­i­folds and Jones–Wit­ten the­ory. Edi­ted by S. K. Don­ald­son and C. B. Thomas. Lon­don Math­em­at­ic­al So­ci­ety Lec­ture Note Series 151. Cam­bridge Uni­versity Press, 1990. MR 1171913 Zbl 0735.​57005 incollection

J. H. Ru­bin­stein and D. A. Thomas: “A vari­ation­al ap­proach to the Stein­er net­work prob­lem,” Ann. Op­er. Res. 33 : 6 (1991), pp. 481–​499. MR 1140992 Zbl 0734.​05040 article

J. H. Ru­bin­stein and D. A. Thomas: “The Stein­er ra­tio con­jec­ture for six points,” J. Comb. The­ory, Ser. A 58 : 1 (September 1991), pp. 54–​77. MR 1119701 Zbl 0739.​05034 article

J. H. Ru­bin­stein, D. A. Thomas, and J. F. Weng: “De­gree-five Stein­er points can­not re­duce net­work costs for planar sets,” Net­works 22 : 6 (1992), pp. 531–​537. MR 1178862 Zbl 0774.​05032 article

J. H. Ru­bin­stein and D. A. Thomas: “The Stein­er ra­tio con­jec­ture for co­cir­cu­lar points,” Dis­crete Com­put. Geom. 7 : 1 (1992), pp. 77–​86. MR 1134454 Zbl 0774.​05031 article

J. H. Ru­bin­stein and D. A. Thomas: “Gra­ham’s prob­lem on shortest net­works for points on a circle,” pp. 193–​218 in The Stein­er prob­lem, published as Al­gorith­mica 7 : 2–​3. Issue edi­ted by F. K. Hwang. 1992. MR 1146495 Zbl 0748.​05051 incollection

I. R. Aitchis­on and J. H. Ru­bin­stein: “Com­bin­at­or­i­al cu­bings, cusps, and the do­deca­hed­ral knots,” pp. 17–​26 in To­po­logy ’90 (Colum­bus, OH, Feb­ru­ary–June 1990). Edi­ted by B. Apanasov, W. D. Neu­mann, A. W. Re­id, and L. Sieben­mann. Ohio State Uni­versity Math­em­at­ic­al Re­search In­sti­tute Pub­lic­a­tions 1. de Gruyter (Ber­lin), 1992. MR 1184399 Zbl 0773.​57010 incollection

J. H. Ru­bin­stein, D. Thomas, and N. Wormald: Al­gorithms for con­strained net­works, 1992. From un­pub­lished pro­ceed­ings of the sev­enth Aus­trali­an tele­traffic re­search sem­in­ar (Man­num, Aus­tralia, Novem­ber 1992). misc

I. R. Aitchis­on, E. Lums­den, and J. H. Ru­bin­stein: “Cusp struc­tures of al­tern­at­ing links,” In­vent. Math. 109 : 1 (1992), pp. 473–​494. MR 1176199 Zbl 0810.​57010 article

I. R. Aitchis­on and J. H. Ru­bin­stein: “Ca­non­ic­al sur­gery on al­tern­at­ing link dia­grams,” pp. 543–​558 in Knots 90 (Osaka, Ja­pan 15–19 Au­gust 1990). Edi­ted by A. Kawau­chi. de Gruyter (Ber­lin), 1992. MR 1177446 Zbl 0765.​57005 incollection

I. R. Aitchis­on and J. H. Ru­bin­stein: “In­com­press­ible sur­faces and the to­po­logy of 3-di­men­sion­al man­i­folds,” J. Aust. Math. Soc., Ser. A 55 : 1 (1993), pp. 1–​22. MR 1231691 Zbl 0813.​57017 article

J. Hass, J. T. Pitts, and J. H. Ru­bin­stein: “Ex­ist­ence of un­stable min­im­al sur­faces in man­i­folds with ho­mo­logy and ap­plic­a­tions to triply peri­od­ic min­im­al sur­faces,” pp. 147–​162 in Dif­fer­en­tial geo­metry (Los Angeles, 8–28 Ju­ly 1990), part 1: Par­tial dif­fer­en­tial equa­tions on man­i­folds. Edi­ted by R. E. Green and S.-T. Yau. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics 54. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1993. MR 1216582 Zbl 0798.​53009 incollection

D. A. Thomas, J. H. Ru­bin­stein, and T. Cole: “The Stein­er min­im­al net­work for con­vex con­fig­ur­a­tions,” Dis­crete Com­put. Geom. 9 : 3 (1993), pp. 323–​333. MR 1204786 Zbl 0774.​05033 article

J. H. Ru­bin­stein: “An al­gorithm to re­cog­nize the 3-sphere,” pp. 601–​611 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Zürich, 3–11 Au­gust 1994), vol. I. Edi­ted by S. D. Chat­terji. Birkhäuser (Basel), 1995. MR 1403961 Zbl 0864.​57009 incollection

J. T. Pitts and J. H. Ru­bin­stein: “The to­po­logy of min­im­al sur­faces in Seifert fiber spaces,” Mich. Math. J. 42 : 3 (1995), pp. 525–​535. MR 1357622 Zbl 0866.​57011 article

H. Ru­bin­stein and M. Schar­le­mann: “Com­par­ing Hee­gaard split­tings of non-Haken 3-man­i­folds,” To­po­logy 35 : 4 (October 1996), pp. 1005–​1026. MR 1404921 Zbl 0858.​57020 article

M. Brazil, T. Cole, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Min­im­al Stein­er trees for \( 2^k\times 2^k \) square lat­tices,” J. Comb. The­ory, Ser. A 73 : 1 (1996), pp. 91–​110. MR 1367609 Zbl 0844.​05036 article

I. R. Aitchis­on and J. H. Ru­bin­stein: “Geodes­ic sur­faces in knot com­ple­ments,” Exp. Math. 6 : 2 (1997), pp. 137–​150. MR 1474574 Zbl 0891.​57017 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Full min­im­al Stein­er trees on lat­tice sets,” J. Com­bin. The­ory Ser. A 78 : 1 (April 1997), pp. 51–​91. MR 1439632 Zbl 0874.​05018 article

D. Mc­Cul­lough and J. H. Ru­bin­stein: The gen­er­al­ized Smale con­jec­ture for 3-man­i­folds with genus-2 one-sided Hee­gaard split­tings. Pre­print, December 1997. ArXiv 9712233 techreport

I. R. Aitchis­on, S. Mat­sumoto, and J. H. Ru­bin­stein: “Im­mersed sur­faces in cubed man­i­folds,” Asi­an J. Math. 1 : 1 (1997), pp. 85–​95. MR 1480991 Zbl 0935.​57033 article

J. H. Ru­bin­stein, D. A. Thomas, and N. C. Wormald: “Stein­er trees for ter­min­als con­strained to curves,” SIAM J. Dis­crete Math. 10 : 1 (1997), pp. 1–​17. MR 1430542 Zbl 0869.​05023 article

J. H. Ru­bin­stein: “Poly­hed­ral min­im­al sur­faces, Hee­gaard split­tings and de­cision prob­lems for 3-di­men­sion­al man­i­folds,” pp. 1–​20 in Geo­met­ric to­po­logy (Athens, GA, 2–13 Au­gust 1993). Edi­ted by W. H. Kazez. AMS/IP Stud­ies in Ad­vanced Math­em­at­ics 2. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1997. MR 1470718 Zbl 0889.​57021 incollection

J. H. Ru­bin­stein and J. F. Weng: “Com­pres­sion the­or­ems and Stein­er ra­tios on spheres,” J. Comb. Op­tim. 1 : 1 (1997), pp. 67–​78. MR 1606181 Zbl 0895.​90173 article

H. Ru­bin­stein and M. Schar­le­mann: “Trans­verse Hee­gaard split­tings,” Mich. Math. J. 44 : 1 (1997), pp. 69–​83. MR 1439669 Zbl 0907.​57013 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Min­im­al Stein­er trees for rect­an­gu­lar ar­rays of lat­tice points,” J. Comb. The­ory, Ser. A 79 : 2 (August 1997), pp. 181–​208. MR 1462554 Zbl 0883.​05038 article

V. Ger­shkovich and H. Ru­bin­stein: “Morse the­ory for Min-type func­tions,” Asi­an J. Math. 1 : 4 (December 1997), pp. 696–​715. MR 1621571 Zbl 0921.​58006 article

Y. Mori­ah and H. Ru­bin­stein: “Hee­gaard struc­tures of neg­at­ively curved 3-man­i­folds,” Com­mun. Anal. Geom. 5 : 3 (1997), pp. 375–​412. MR 1487722 Zbl 0890.​57025 article

H. Ru­bin­stein and M. Schar­le­mann: “Com­par­ing Hee­gaard split­tings: The bounded case,” Trans. Am. Math. Soc. 350 : 2 (1998), pp. 689–​715. MR 1401528 Zbl 0892.​57009 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Shortest net­works on spheres,” pp. 453–​461 in Net­work design: Con­nectiv­ity and fa­cil­it­ies loc­a­tion (Prin­ceton, NJ, 28–30 April 1997). Edi­ted by P. M. Pardalos and D.-Z. Du. DIMACS Series in Dis­crete Math­em­at­ics and The­or­et­ic­al Com­puter Sci­ence 40. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1998. MR 1613017 Zbl 0915.​05043 incollection

I. R. Aitchis­on, S. Mat­sumoto, and J. H. Ru­bin­stein: “Sur­faces in the fig­ure-8 knot com­ple­ment,” J. Knot The­ory Rami­fic­a­tions 7 : 8 (1998), pp. 1005–​1025. MR 1671559 Zbl 0924.​57018 article

J. H. Ru­bin­stein and S. Wang: “\( \pi_1 \)-in­ject­ive sur­faces in graph man­i­folds,” Com­ment. Math. Helv. 73 : 4 (1998), pp. 499–​515. MR 1639876 Zbl 0916.​57001 article

H. Ru­bin­stein and M. Sageev: “In­ter­sec­tion pat­terns of es­sen­tial sur­faces in 3-man­i­folds,” To­po­logy 38 : 6 (1999), pp. 1281–​1291. MR 1690158 Zbl 1115.​57301 article

I. R. Aitchis­on and J. H. Ru­bin­stein: “Com­bin­at­or­i­al Dehn sur­gery on cubed and Haken 3-man­i­folds,” pp. 1–​21 in Pro­ceed­ings of the Kirby­Fest (Berke­ley, CA, 22–26 June 1998). Edi­ted by J. Hass and M. Schar­le­mann. Geo­metry & To­po­logy Mono­graphs 2. In­ter­na­tion­al Press (Cam­bridge, MA), 1999. Pa­pers ded­ic­ated to Rob Kirby on the oc­ca­sion of his 60th birth­day. MR 1734399 Zbl 0948.​57016 ArXiv 9911072 incollection

I. R. Aitchis­on, S. Mat­sumoto, and J. H. Ru­bin­stein: “Dehn sur­gery on the fig­ure 8 knot: Im­mersed sur­faces,” Proc. Am. Math. Soc. 127 : 8 (1999), pp. 2437–​2442. MR 1485454 Zbl 0926.​57006 article

H. Ru­bin­stein and M. Sageev: “Es­sen­tial sur­faces and tame­ness of cov­ers,” Mich. Math. J. 46 : 1 (1999), pp. 83–​92. MR 1682889 Zbl 0959.​57002 article

I. R. Aitchis­on and J. H. Ru­bin­stein: “Poly­hed­ral met­rics and 3-man­i­folds which are vir­tu­al bundles,” Bull. Lon­don Math. Soc. 31 : 1 (1999), pp. 90–​96. MR 1651060 Zbl 0930.​57015 article

H. Ru­bin­stein and M. Schar­le­mann: “Genus two Hee­gaard split­tings of ori­ent­able three-man­i­folds,” pp. 489–​553 in Pro­ceed­ings of the Kirby­Fest (Berke­ley, CA, 22–26 June 1998). Edi­ted by J. Hass and M. Schar­le­mann. Geo­metry & To­po­logy Mono­graphs 2. In­ter­na­tion­al Press (Cam­bridge, MA), 1999. Pa­pers ded­ic­ated to Rob Kirby on the oc­ca­sion of his 60th birth­day. MR 1734422 Zbl 0962.​57013 ArXiv 9712262 incollection

J. F. Weng and J. H. Ru­bin­stein: “A note on the com­pres­sion the­or­em for con­vex sur­faces,” pp. 257–​260 in Com­bin­at­or­ics and ap­plic­a­tions (Tianjin, China, 28–30 June 1996), published as Dis­crete Math. 212 : 3. Issue edi­ted by W. Y. C. Chen, D.-Z. Du, F. D. Hsu, and H. P. Yap. February 2000. MR 1748655 Zbl 0986.​90047 incollection

Ad­vances in Stein­er trees. Edi­ted by D.-Z. Du, J. M. Smith, and J. H. Ru­bin­stein. Com­bin­at­or­i­al Op­tim­iz­a­tion 6. Kluwer Aca­dem­ic (Dordrecht), 2000. MR 1758343 Zbl 0932.​00010 book

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, and J. F. Weng: Mod­el­ling and op­tim­isa­tion of a weighted net­work in an un­der­ground mine design, 2001. From un­pub­lished pro­ceed­ings of the third in­ter­na­tion­al con­fer­ence on con­trol the­ory and ap­plic­a­tions (Pre­tor­ia, South Africa, 12–14 Decem­ber 2001). misc

J. H. Ru­bin­stein, D. A. Thomas, and N. C. Wormald: “A poly­no­mi­al al­gorithm for a con­strained trav­el­ing sales­man prob­lem,” Net­works 38 : 2 (September 2001), pp. 68–​75. MR 1852365 Zbl 0990.​90102 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Gradi­ent-con­strained min­im­um net­works, I: Fun­da­ment­als,” J. Glob. Op­tim. 21 : 2 (2001), pp. 139–​155. Part III was pub­lished in J. Op­tim. The­ory Ap­pl. 155:1 (2012). Ru­bin­stein was not a co-au­thor of part II. MR 1863330 Zbl 1068.​90605 article

J. H. Ru­bin­stein, D. A. Thomas, and J. Weng: “Min­im­um net­works for four points in space,” Geom. Ded­icata 93 : 1 (2002), pp. 57–​70. MR 1934686 Zbl 1009.​05042 article

W. Jaco, D. Letscher, and J. H. Ru­bin­stein: “Al­gorithms for es­sen­tial sur­faces in 3-man­i­folds,” pp. 107–​124 in To­po­logy and geo­metry: Com­mem­or­at­ing SIS­T­AG (Na­tion­al Uni­versity of Singa­pore, 2–6 Ju­ly 2001). Edi­ted by A. J. Ber­rick, M. C. Leung, and X. Xu. Con­tem­por­ary Math­em­at­ics 314. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2002. Singa­pore In­ter­na­tion­al Sym­posi­um in To­po­logy and Geo­metry. MR 1941626 Zbl 1012.​57029 incollection

M. Brazil, D. Lee, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “A net­work mod­el to op­tim­ise cost in un­der­ground mine design,” Trans. S. Afr. Inst. Elec­tr. Eng. 93 : 2 (2002), pp. 97–​103. article

J. Hass, P. Nor­bury, and J. H. Ru­bin­stein: “Min­im­al spheres of ar­bit­rar­ily high Morse in­dex,” Com­mun. Anal. Geom. 11 : 3 (2003), pp. 425–​439. MR 2015753 Zbl 1104.​53055 ArXiv 0206286 article

J. H. Ru­bin­stein: “Tri­an­gu­la­tions of 3-man­i­folds,” pp. 74–​77 in Low di­men­sion­al to­po­logy (Morn­ing­side Cen­ter of Math­em­at­ics, Beijing, 1998–1999). Edi­ted by B. Li, S. Wang, and X. Zhao. New Stud­ies in Ad­vanced Math­em­at­ics 3. In­ter­na­tion­al Press (Somerville, MA), 2003. MR 2052248 Zbl 1047.​57011 incollection

J. H. Ru­bin­stein: “Com­par­ing open-book and Hee­gaard de­com­pos­i­tions of 3-man­i­folds,” pp. 189–​196 in Pro­ceed­ings of Gökova geo­metry-to­po­logy con­fer­ence 2002 (Gökova, Tur­key, 27 May–31 May, 2002), published as Turk. J. Math. 27 : 1. Issue edi­ted by S. Ak­bu­lut, T. Önder, and R. J. Stern. Sci­entif­ic and Tech­nic­al Re­search Coun­cil of Tur­key (Ank­ara), 2003. MR 1975338 Zbl 1045.​57008 incollection

W. Jaco and J. H. Ru­bin­stein: “0-ef­fi­cient tri­an­gu­la­tions of 3-man­i­folds,” J. Dif­fer. Geom. 65 : 1 (2003), pp. 61–​168. MR 2057531 Zbl 1068.​57023 ArXiv 0207158 article

J. H. Ru­bin­stein: “Poly­hed­ral geo­metry,” pp. 69–​73 in Low di­men­sion­al to­po­logy (Morn­ing­side Cen­ter of Math­em­at­ics, Beijing, 1998–1999). Edi­ted by B. Li, S. Wang, and X. Zhao. New Stud­ies in Ad­vanced Math­em­at­ics 3. In­ter­na­tion­al Press (Som­merville, MA), 2003. MR 2052247 Zbl 1055.​52012 incollection

J. H. Ru­bin­stein: “Dehn’s lemma and the loop the­or­em,” pp. 61–​68 in Low di­men­sion­al to­po­logy (Morn­ing­side Cen­ter of Math­em­at­ics, Beijing, 1998–1999). Edi­ted by B. Li, S. Wang, and X. Zhao. New Stud­ies in Ad­vanced Math­em­at­ics 3. In­ter­na­tion­al Press (Som­merville, MA), 2003. MR 2052246 Zbl 1056.​57013 incollection

J. Ma­h­er and J. H. Ru­bin­stein: “Peri­od three ac­tions on the three-sphere,” Geom. To­pol. 7 (2003), pp. 329–​397. MR 1988290 Zbl 1037.​57012 ArXiv 0204077 article

M. Brazil, D. Lee, M. Van Leuven, J. H. Ru­bin­stein, D. A. Thomas, and N. C. Wormald: “Op­tim­ising de­clines in un­der­ground mines,” Min­ing Tech. 112 : 3 (2003), pp. 164–​170. article

J. H. Ru­bin­stein: “An al­gorithm to re­cog­nise small Seifert fiber spaces,” Turk­ish J. Math. 28 : 1 (2004), pp. 75–​87. MR 2056761 Zbl 1061.​57023 article

S. Hong, D. Mc­Cul­lough, and J. H. Ru­bin­stein: The Smale con­jec­ture for lens spaces. Pre­print, October 2004. ArXiv 0411016 techreport

E. Kang and J. H. Ru­bin­stein: “Ideal tri­an­gu­la­tions of 3-man­i­folds, I. Spun nor­mal sur­face the­ory,” pp. 235–​265 in Pro­ceed­ings of the Cas­son Fest: Arkan­sas and Texas 2003 (Fay­etteville, AR, 10–12 April 2003 and Aus­tin, TX, 19–21 May 2003). Edi­ted by C. Gor­don and Y. Rieck. Geo­metry & To­po­logy Mono­graphs 7. Math­em­at­ic­al Sci­ences Pub­lish­ers (Berke­ley, CA), 2004. Part II was pub­lished in Al­gebr. Geom. To­pol. 5 (2005). MR 2172486 Zbl 1085.​57016 ArXiv 0410541 incollection

I. R. Aitchis­on and J. H. Ru­bin­stein: “Loc­al­ising Dehn’s lemma and the loop the­or­em in 3-man­i­folds,” Math. Proc. Camb. Philos. Soc. 137 : 2 (2004), pp. 281–​292. MR 2092060 Zbl 1067.​57009 article

M. Boileau, J. H. Ru­bin­stein, and S. Wang: Fi­nite­ness of 3-man­i­folds as­so­ci­ated with non zero de­gree map­pings. Pre­print, 2005. ArXiv 0511541 techreport

J. H. Ru­bin­stein and R. Sin­clair: “Visu­al­iz­ing Ricci flow of man­i­folds of re­volu­tion,” Exp. Math. 14 : 3 (2005), pp. 285–​298. MR 2172707 Zbl 1081.​53055 ArXiv 0406189 article

M. Brazil, D. A. Thomas, J. F. Weng, J. H. Ru­bin­stein, and D. H. Lee: “Cost op­tim­isa­tion for un­der­ground min­ing net­works,” Op­tim. Eng. 6 : 2 (2005), pp. 241–​256. MR 2136609 Zbl 1093.​90067 article

E. Kang and J. H. Ru­bin­stein: “Ideal tri­an­gu­la­tions of 3-man­i­folds, II: Taut and angle struc­tures,” Al­gebr. Geom. To­pol. 5 (2005), pp. 1505–​1533. Part I was pub­lished in Pro­ceed­ings of the Cas­son Fest (2004). MR 2186107 Zbl 1096.​57018 ArXiv 0502437 article

M. Brazil, J. H. Ru­bin­stein, and M. Volz: “The gradi­ent con­strained Fer­mat–Weber prob­lem for un­der­ground mine design,” pp. 16–​23 in Pro­ceed­ings of the 18th na­tion­al con­fer­ence of the Aus­trali­an So­ci­ety for Op­er­a­tions Re­search and the 11th Aus­trali­an op­tim­isa­tion day (Perth, Septem­ber 2005). Edi­ted by L. Cac­cetta and V. Re­hbock. 2005. incollection

M. Brazil, D. Lee, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Op­tim­isa­tion in the design of un­der­ground mine ac­cess,” pp. 121–​124 in Orebody mod­el­ling and stra­tegic mine plan­ning: Un­cer­tainty and risk man­age­ment mod­els. Edi­ted by R. Di­mitrako­poulos. Spec­trum Series 14. Aus­tralasi­an In­sti­tute of Min­ing and Me­tal­lurgy (Mel­bourne), 2005. incollection

J. H. Ru­bin­stein: “Shortest net­works in 2 and 3 di­men­sions,” pp. 783–​790 in Glob­al the­ory of min­im­al sur­faces (Berke­ley, CA, 25 June–27 Ju­ly 2001). Edi­ted by D. A. Hoff­man. Clay Math­em­at­ics Pro­ceed­ings 2. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2005. Pro­ceed­ings of the Clay Math­em­at­ics In­sti­tute 2001 sum­mer school. MR 2167290 Zbl 1101.​05026 incollection

P. Nor­bury and J. H. Ru­bin­stein: “Closed geodesics on in­com­plete sur­faces,” Geom. Ded­icata 116 : 1 (2005), pp. 1–​36. MR 2195439 Zbl 1096.​53006 ArXiv 0309159 article

J. H. Ru­bin­stein: “Min­im­al sur­faces in geo­met­ric 3-man­i­folds,” pp. 725–​746 in Glob­al the­ory of min­im­al sur­faces (Berke­ley, CA, 25 June–27 Ju­ly 2001). Edi­ted by D. A. Hoff­man. Clay Math­em­at­ics Pro­ceed­ings 2. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2005. Pro­ceed­ings of the Clay Math­em­at­ics In­sti­tute 2001 sum­mer school. MR 2167286 Zbl 1119.​53042 incollection

L. Bar­to­lini and J. H. Ru­bin­stein: “One-sided Hee­gaard split­tings of \( \mathbb{R}P^3 \),” Al­gebr. Geom. To­pol. 6 (2006), pp. 1319–​1330. MR 2253448 Zbl 1133.​57005 article

W. Jaco and J. H. Ru­bin­stein: Layered-tri­an­gu­la­tions of 3-man­i­folds. Pre­print, March 2006. ArXiv 0603601 techreport

J. Cof­fey and J. H. Ru­bin­stein: 3-man­i­folds built from in­ject­ive handle­bod­ies. Pre­print, January 2006. ArXiv 0601718 techreport

J. H. Ru­bin­stein, J. Weng, and N. Wormald: “Ap­prox­im­a­tions and lower bounds for the length of min­im­al Eu­c­lidean Stein­er trees,” J. Glob. Op­tim. 35 : 4 (2006), pp. 573–​592. MR 2249549 Zbl 1133.​90408 article

B. I. P. Ru­bin­stein, P. L. Bart­lett, and J. H. Ru­bin­stein: “Shift­ing, one-in­clu­sion mis­take bounds and tight mul­ti­class ex­pec­ted risk bounds,” pp. 1193–​1200 in NIPS: Pro­ceed­ings of the 2006 con­fer­ence (Van­couver, 4–7 Decem­ber 2006). Edi­ted by B. Schölkopf, J. C. Platt, and T. Hof­mann. Ad­vances in Neur­al In­form­a­tion Pro­cessing Sys­tems 19. MIT Press (Cam­bridge, MA), 2007. incollection

B. I. P. Ru­bin­stein, P. Bart­lett, and J. H. Ru­bin­stein: Shift­ing: One in­clu­sion mis­take bounds and sample com­pres­sion. Technical report UCB/EECS-2007-86, EECS De­part­ment, UC-Berke­ley, 25 June 2007. Pre­print of an art­icle pub­lished in J. Com­put. Syst. Sci. 75:1 (2009). techreport

J. John­son and J. H. Ru­bin­stein: Auto­morph­isms of Hee­gaard split­tings of 3-man­i­folds. Pre­print, 2007. techreport

J. H. Ru­bin­stein: “Prob­lems around 3-man­i­folds,” pp. 285–​298 in Work­shop on Hee­gaard split­tings (Tech­nion, Haifa, Is­rael, sum­mer 2005). Edi­ted by C. Gor­don and Y. Mori­ah. Geo­metry & To­po­logy Mono­graphs 12. Math­em­at­ic­al Sci­ences Pub­lish­ers (Berke­ley, CA), 2007. MR 2408251 Zbl 1139.​57019 ArXiv 0904.​0017 incollection

M. Brazil, P. A. Gross­man, D. H. Lee, J. H. Ru­bin­stein, D. A. Thomas, and N. C. Wormald: “De­cline design in un­der­ground mines us­ing con­strained path op­tim­isa­tion,” Min­ing Tech. 117 : 2 (2008), pp. 93–​99. article

M. Brazil, P. A. Gross­man, D. A. Thomas, J. H. Ru­bin­stein, D. Lee, and N. C. Wormald: “Con­strained path op­tim­isa­tion for un­der­ground mine lay­out,” pp. 856–​861 in Pro­ceed­ings of the World Con­gress on En­gin­eer­ing 2007 (Im­per­i­al Col­lege, Lon­don, 2–4 Ju­ly 2007), vol. II. Edi­ted by S. I. Ao, L. Gel­man, D. Hukins, A. Hunter, and A. M. Kor­sun­sky. Lec­ture Notes in En­gin­eer­ing and Com­puter Sci­ence 2166. News­wood Lim­ited (Hong Kong), 2008. incollection

B. I. P. Ru­bin­stein, P. L. Bart­lett, and J. H. Ru­bin­stein: “Shift­ing: one-in­clu­sion mis­take bounds and sample com­pres­sion,” J. Com­put. Syst. Sci. 75 : 1 (2009), pp. 37–​59. A cor­ri­gendum was pub­lished in J. Com­put. Syst. Sci. 76:3–4 (2010). MR 2472316 Zbl 1158.​68452 article

C. Ay, J.-M. Richard, and J. H. Ru­bin­stein: “Sta­bil­ity of asym­met­ric tet­ra­quarks in the min­im­al-path lin­ear po­ten­tial,” Phys. Lett. B 674 : 3 (April 2009), pp. 8. ArXiv 0901.​3022 article

W. Jaco, J. H. Ru­bin­stein, and S. Till­mann: \( \mathbb{Z}_2 \)-Thur­ston norm and com­plex­ity of 3-man­i­folds. Pre­print, June 2009. ArXiv 0906.​4864 techreport

W. Jaco, H. Ru­bin­stein, and S. Till­mann: “Min­im­al tri­an­gu­la­tions for an in­fin­ite fam­ily of lens spaces,” J. To­pol. 2 : 1 (2009), pp. 157–​180. MR 2499441 Zbl 1227.​57026 ArXiv 0805.​2425 article

J. Hass, J. H. Ru­bin­stein, and A. Thompson: “Knots and \( k \)-width,” Geom. Ded­icata 143 : 1 (2009), pp. 7–​18. MR 2576289 Zbl 1189.​57005 ArXiv 0604256 article

B. I. P. Ru­bin­stein, P. L. Bart­lett, and J. H. Ru­bin­stein: “Shift­ing: One in­clu­sion mis­take bounds and sample com­pres­sion,” J. Com­put. Syst. Sci. 75 : 1 (2009), pp. 39–​75. A pre­print of this art­icle was pub­lished in 2007. article

Y. Rieck and J. H. Ru­bin­stein: “In­vari­ant Hee­gaard sur­faces in man­i­folds with in­vol­u­tions and the Hee­gaard genus of double cov­ers,” Com­mun. Anal. Geom. 17 : 5 (2009), pp. 851–​901. MR 2643734 Zbl 1222.​57014 ArXiv 0607145 article

W. Jaco, J. H. Ru­bin­stein, and E. Sedg­wick: “Find­ing planar sur­faces in knot- and link-man­i­folds,” J. Knot The­ory Rami­fic­a­tions 18 : 3 (2009), pp. 397–​446. MR 2514851 Zbl 1176.​57024 ArXiv 0608700 article

B. I. P. Ru­bin­stein, P. L. Bart­lett, and J. H. Ru­bin­stein: “Cor­ri­gendum to ‘Shift­ing: One-in­clu­sion mis­take bounds and sample com­pres­sion’,” J. Com­put. Syst. Sci. 76 : 3–​4 (May–June 2010), pp. 278–​280. Cor­ri­gendum to an art­icle pub­lished in J. Com­put. Syst. Sci. 75:1 (2009). MR 2656493 Zbl 1201.​68103 article

J. H. Ru­bin­stein: “Prob­lems at the Jac­ofest,” pp. 195–​196 in To­po­logy and geo­metry in di­men­sion three: Tri­an­gu­la­tions, in­vari­ants, and geo­met­ric struc­tures (Ok­lahoma State Uni­versity, Still­wa­ter, OK, 4–6 June 2010). Edi­ted by W. Li, L. Bar­to­lini, J. John­son, F. Luo, R. My­ers, and J. H. Ru­bin­stein. Con­tem­por­ary Math­em­at­ics 560. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2011. Con­fer­ence in hon­or of Wil­li­am Jaco’s 70th birth­day. MR 2866932 incollection

To­po­logy and geo­metry in di­men­sion three: Tri­an­gu­la­tions, in­vari­ants, and geo­met­ric struc­tures (Ok­lahoma State Uni­versity, Still­wa­ter, OK, 4–6 June 2010). Edi­ted by W. Li, L. Bar­to­lini, J. John­son, F. Luo, R. My­ers, and J. H. Ru­bin­stein. Con­tem­por­ary Math­em­at­ics 560. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2011. Con­fer­ence in hon­or of Wil­li­am Jaco’s 70th birth­day. MR 2866933 Zbl 1231.​57001 book

P. Hall: “In­ter­view with Hyam Ru­bin­stein,” Asia Pac. Math. Newsl. 1 : 4 (2011), pp. 3. MR 2896469 article

W. Jaco and J. H. Ru­bin­stein: An­nu­lar-ef­fi­cient tri­an­gu­la­tions of 3-man­i­folds. Pre­print, August 2011. ArXiv 1108.​2936 techreport

M. Oz­a­wa and J. H. Ru­bin­stein: On the Neuwirth con­jec­ture for knots. Pre­print, March 2011. ArXiv 1103.​2576 techreport

C. D. Hodg­son, J. H. Ru­bin­stein, H. Se­ger­man, and S. Till­mann: “Veer­ing tri­an­gu­la­tions ad­mit strict angle struc­tures,” Geom. To­pol. 15 : 4 (2011), pp. 2073–​2089. MR 2860987 Zbl 1246.​57034 article

W. Jaco, J. H. Ru­bin­stein, and S. Till­mann: “Cov­er­ings and min­im­al tri­an­gu­la­tions of 3-man­i­folds,” Al­gebr. Geom. To­pol. 11 : 3 (2011), pp. 1257–​1265. MR 2801418 Zbl 1229.​57010 ArXiv 0903.​0112 article

B. Foozwell and H. Ru­bin­stein: “In­tro­duc­tion to the the­ory of Haken \( n \)-man­i­folds,” pp. 71–​84 in To­po­logy and geo­metry in di­men­sion three: Tri­an­gu­la­tions, in­vari­ants, and geo­met­ric struc­tures (Ok­lahoma State Uni­versity, Still­wa­ter, OK, 4–6 June 2010). Edi­ted by W. Li, L. Bar­to­lini, J. John­son, F. Luo, R. My­ers, and J. H. Ru­bin­stein. Con­tem­por­ary Math­em­at­ics 560. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2011. Con­fer­ence in hon­or of Wil­li­am Jaco’s 70th birth­day. MR 2866924 incollection

S. Hong, J. Kal­lion­gis, D. Mc­Cul­lough, and J. H. Ru­bin­stein: Dif­feo­morph­isms of el­lipt­ic 3-man­i­folds. Lec­ture Notes in Math­em­at­ics 2055. Spring­er (Ber­lin), 2012. MR 2976322 Zbl 06062046 ArXiv 1110.​4996 book

A. J. Chang, M. Brazil, J. H. Ru­bin­stein, and D. A. Thomas: “Curvature-con­strained dir­ec­tion­al-cost paths in the plane,” J. Glob. Op­tim. 53 : 4 (2012), pp. 663–​681. MR 2944057 Zbl 06117793 article

C. D. Hodg­son, J. H. Ru­bin­stein, and H. Se­ger­man: “Tri­an­gu­la­tions of hy­per­bol­ic 3-man­i­folds ad­mit­ting strict angle struc­tures,” J. To­pol. 5 : 4 (2012), pp. 887–​908. Zbl 06121970 ArXiv 1111.​3168 article

B. A. Bur­ton, J. H. Ru­bin­stein, and S. Till­mann: “The Weber–Seifert do­deca­hed­ral space is non-Haken,” Trans. Am. Math. Soc. 364 : 2 (2012), pp. 911–​932. MR 2846358 Zbl 1250.​57033 ArXiv 0909.​4625 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. Wormald: “Gradi­ent-con­strained min­im­um net­works, III: Fixed to­po­logy,” J. Op­tim. The­ory Ap­pl. 155 : 1 (2012), pp. 336–​354. Part I was pub­lished in J. Glob. Op­tim. 21:2 (2001). Ru­bin­stein was not a co-au­thor of part II. MR 2983123 Zbl 1255.​90120 article

B. I. P. Ru­bin­stein and J. H. Ru­bin­stein: “A geo­met­ric ap­proach to sample com­pres­sion,” J. Mach. Learn. Res. 13 (April 2012), pp. 1221–​1261. MR 2930638 ArXiv 0911.​3633 article

W. H. Jaco and J. H. Ru­bin­stein: In­fla­tions of ideal tri­an­gu­la­tions. Pre­print, February 2013. ArXiv 1302.​6921 techreport