Minimal Volume Alexandrov Spaces
Minimal Volume Alexandrov Spaces
复制标题
最小体积亚历山德罗夫空间
DOI：
10.4310/jdg/1090351384
复制
发表时间：
2001
影响因子：
2.5
通讯作者：
Peter A. Storm
中科院分区：
文献类型：
--
作者：
Peter A. Storm
证明了闭双曲流形在同一bilipschitz类中曲率下界为-1的所有Alexandrov空间上体积最小。作为一个推论，证明了具有完全测地边界的紧致凸核在同一bilipschitz类的所有双曲流形上体积最小。同时，闭合双曲流形在同一bilipschitz类中锥角不大于2的所有双曲锥流形上体积最小。这个证明使用了贝松-库尔图瓦-加洛开发的技术。在三维空间中，给出了关于非圆柱形流形的Kleinian群猜想的部分解。
Closed hyperbolic manifolds are proven to minimize volume over all Alexandrov spaces with curvature bounded below by -1 in the same bilipschitz class. As a corollary compact convex cores with totally geodesic boundary are proven to minimize volume over all hyperbolic manifolds in the same bilipschitz class. Also, closed hyperbolic manifolds minimize volume over all hyperbolic cone manifolds in the same bilipschitz class with cone angles not greater than 2pi. The proof uses techniques developed by Besson-Courtois-Gallot. In 3 dimensions, this result provides a partial solution to a conjecture in Kleinian groups concerning acylindrical manifolds.