Hyperbolization of cusps with convex boundary

Fillastre, François; Izmestiev, Ivan; Veronelli, Giona

doi:10.1007/s00229-015-0814-y

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Journal article

Hyperbolization of cusps with convex boundary

Fillastre, François Université de Cergy-Pontoise, UMR CNRS 8088, 95000, Cergy-Pontoise, France
Izmestiev, Ivan Département de mathématiques, Université de Fribourg, Switzerland
Veronelli, Giona Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), Villetaneuse, France

04.01.2016

Published in:

Manuscripta Mathematica. - 2016, vol. 150, no. 3–4, p. 475–492

English We prove that for every metric on the torus with curvature bounded from below by −1 in the sense of Alexandrov there exists a hyperbolic cusp with convex boundary such that the induced metric on the boundary is the given metric. The proof is by polyhedral approximation. This was the last open case of a general theorem: every metric with curvature bounded from below on a compact surface is isometric to a convex surface in a 3-dimensional space form.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language