凸边界尖点的双曲化
Hyperbolization of cusps with convex boundary
摘要：
证明了对于曲率从下面有界为-1的Alexandrov意义下的环面上的每个度量，存在一个凸边界的双曲尖点，使得边界上的诱导度量是给定的度量.证明是通过多面体近似。这是一个一般定理的最后一个公开的例子：在一个紧致曲面上，每个曲率从下到上有界的度量都等距于一个三维空间型中的凸曲面。
英文摘要：
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.
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