关于3维负曲率流形的拓扑型(英文)

On the Topological Type of 3-dimensional Negatively Curved Manifolds

本文的主要定理是:对每一个正数V,存在一个D>0,如果一个3维黎曼流形M的体积小于V,截面曲率在-1和0之间,而且直径大于D,那么M允许一个双曲结构。

The main theorem in this paper is the following: for any positive number V, there is a D>0.such that any 3-dimensional Riemannian manifold M with volume not larger than V, sectional curvature between -1 and 0, and diameter larger than D admits a hyperbolic structure.