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
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/305024
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