Hyperbolization of cusps with convex boundary
Metric Geometry
2015-12-15 v2 Differential Geometry
Abstract
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.
Cite
@article{arxiv.1505.04412,
title = {Hyperbolization of cusps with convex boundary},
author = {François Fillastre and Ivan Izmestiev and Giona Veronelli},
journal= {arXiv preprint arXiv:1505.04412},
year = {2015}
}