Fillastre, François Izmestiev, Ivan Veronelli, Giona 2016-01-04 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. application/pdf https://folia.unifr.ch/global/documents/305024 https://folia.unifr.ch/documents/305024/files/izm_hcc.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00229-015-0814-y info:eu-repo/semantics/openAccess License undefined Manuscripta Mathematica. - 2016, vol. 150, no. 3–4, p. 475–492 info:eu-repo/classification/udc/51 Hyperbolization of cusps with convex boundary http://purl.org/coar/resource_type/c_6501