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Volume and rigidity of hyperbolic polyhedral 3‐manifolds
Author(s) -
Luo Feng,
Yang Tian
Publication year - 2018
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/topo.12046
Subject(s) - mathematics , rigidity (electromagnetism) , ideal (ethics) , hyperbolic manifold , pure mathematics , hyperbolic triangle , isometry (riemannian geometry) , hyperbolic group , hyperbolic 3 manifold , curvature , metric (unit) , mathematical analysis , hyperbolic function , geometry , philosophy , operations management , structural engineering , epistemology , engineering , economics
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.