Celebratio Mathematica — Neumann

Contributions on Lipschitz geometry of complex singularities

Works connected to Helge Møller Pedersen

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W. D. Neumann, H. M. Pedersen, and A. Pichon: “A characterization of Lipschitz normally embedded surface singularities,” J. Lond. Math. Soc. (2) 101 : 2 (2020), pp. 612–640. MR 4093968 Zbl 1441.14015 ArXiv 1806.11240 article

Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. These two metrics are in general nonequivalent up to bilipschitz homeomorphism. We give a necessary and sufficient condition for a normal surface singularity to be Lipschitz normally embedded (LNE), that is, to have bilipschitz equivalent outer and inner metrics. In a partner paper (Neumann, Pedersen and Pichon, J. London Math. Soc. (2020)), we apply it to prove that rational surface singularities are LNE if and only if they are minimal.

Anne Pichon	Related
Helge Møller Pedersen	Related

W. D. Neumann, H. M. Pedersen, and A. Pichon: “Minimal surface singularities are Lipschitz normally embedded,” J. Lond. Math. Soc. (2) 101 : 2 (2020), pp. 641–658. MR 4093969 Zbl 1441.14016 ArXiv 1503.03301 article

Anne Pichon	Related
Helge Møller Pedersen	Related