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
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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
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 277376
- DOI 10.1007/s00229-015-0814-y
- Persistent URL
- https://folia.unifr.ch/unifr/documents/305024
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