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Volume and rigidity of hyperbolic polyhedral 3manifolds

Feng Luo Tian Yang

Geometric Analysis and Geometric Topology mathscidoc:1912.43795

Journal of Topology, 11, (1), 1-29, 2018.3
We investigate the rigidity of hyperbolic cone metrics on 3manifolds which are isometric gluing of ideal and hyperideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyperideal hyperbolic polyhedral metrics. It is shown that a hyperideal 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.
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@inproceedings{feng2018volume,
  title={Volume and rigidity of hyperbolic polyhedral 3manifolds},
  author={Feng Luo, and Tian Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205845315106359},
  booktitle={Journal of Topology},
  volume={11},
  number={1},
  pages={1-29},
  year={2018},
}
Feng Luo, and Tian Yang. Volume and rigidity of hyperbolic polyhedral 3manifolds. 2018. Vol. 11. In Journal of Topology. pp.1-29. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205845315106359.
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