Celebratio Mathematica — Chern

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Works connected to Louis Nirenberg

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incollection S. S. Chern, H. I. Levine, and L. Nirenberg: “Intrinsic norms on a complex manifold,” pp. 119–139 in Global analysis: Papers in Honor of K. Kodaira. Edited by D. C. Spencer. University Tokyo Press, 1969. MR 0254877 Zbl 0202.11603

We propose to define in this paper certain norms (or more precisely, semi-norms) on the homology groups of a complex manifold. They will be invariants of the complex strucgture and do not increase under holomorphic mappings. Their definitions depend on the bounded plurisubharmonic functions on the manifold and are modelled after the notion of harmonic length introduced by H. Landau and R. Osserman [1959–1960] for Riemann surfaces (= one-dimensional complex manifolds). It is possible to extend the definition to certain families of chains. In particular we get in this way an intrinsic pseudo-metric on the manifold which is closely related to that of Carathéodory [1927] and to one recently introduced by S. Kobayashi [1967].

Kunihiko Kodaira	Related
Harold I. Levine	Related
Louis Nirenberg	Related
Donald Clayton Spencer	Related

incollection L. Nirenberg: “Some personal remarks about S. S. Chern,” pp. 98–101 in S. S. Chern: A great geometer of the twentieth century. Edited by S.-T. Yau. Monographs in geometry and topology. International Press (Hong Kong), 1992. MR 1201347

Louis Nirenberg	Related
Shing-Tung Yau	Related