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Volume maximization and the extended hyperbolic space

Feng Luo Jean-Marc Schlenker

Geometric Analysis and Geometric Topology mathscidoc:1912.43819

Proceedings of the American Mathematical Society, 140, (3), 1053-1068, 2012
We consider a volume maximization program to construct hyperbolic structures on triangulated 3-manifolds, for which previous progress has lead to consider angle assignments which do not correspond to a hyperbolic metric on each simplex. We show that critical points of the generalized volume are associated to geometric structures modeled on the extended hyperbolic space-the natural extension of hyperbolic space by the de Sitter space-except for the degenerate case where all simplices are Euclidean in a generalized sense.
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@inproceedings{feng2012volume,
  title={Volume maximization and the extended hyperbolic space},
  author={Feng Luo, and Jean-Marc Schlenker},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210004323133383},
  booktitle={Proceedings of the American Mathematical Society},
  volume={140},
  number={3},
  pages={1053-1068},
  year={2012},
}
Feng Luo, and Jean-Marc Schlenker. Volume maximization and the extended hyperbolic space. 2012. Vol. 140. In Proceedings of the American Mathematical Society. pp.1053-1068. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210004323133383.
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