Volume and rigidity of hyperbolic polyhedral 3-manifolds: VOLUME AND RIGIDITY OF HYPERBOLIC POLYHEDRAL 3-MANIFOLDS
Volume and rigidity of hyperbolic polyhedral 3-manifolds: VOLUME AND RIGIDITY OF HYPERBOLIC POLYHEDRAL 3-MANIFOLDS
复制标题
双曲多面体 3-流形的体积和刚度：双曲多面体 3-流形的体积和刚度
DOI：
10.1112/topo.12046
复制
发表时间：
2018
影响因子：
1.1
通讯作者：
Yang, Tian
中科院分区：
文献类型：
--
作者：
Luo, Feng;Yang, Tian
我们研究了三维流形上的双曲锥度量的刚性，三维流形是双曲空间中理想和超理想四面体的等距胶合。这些度量将被称为理想和超理想双曲多面体度量。证明了一个超理想双曲多面体度量在等距上由它的曲率决定，一个修饰的理想双曲多面体度量在等距和修饰的变化上由它的曲率决定。证明中使用的主要工具是体积函数的Fenchel对偶。
We investigate the rigidity of hyperbolic cone metrics on 3‐manifolds which are isometric gluing of ideal and hyper‐ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper‐ideal hyperbolic polyhedral metrics. It is shown that a hyper‐ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is determined up to isometry and change of decorations by its curvature. The main tool used in the proof is the Fenchel dual of the volume function.