Volume maximization and the extended hyperbolic space (Q2880667)
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scientific article; zbMATH DE number 6024113
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Volume maximization and the extended hyperbolic space |
scientific article; zbMATH DE number 6024113 |
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Volume maximization and the extended hyperbolic space (English)
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13 April 2012
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volume functional
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angle structure
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de Sitter space
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0.92293805
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0.8973014
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0.8891578
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0.8846314
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Given an angle structure on a triangulation of a 3-manifold, Casson-Rivin (for a 3-manifold with torus boundary) and Luo (for closed 3 manifolds) defined a naturally associated hyperbolic volume.NEWLINENEWLINEIn the paper under review, the authors investigate the relationship between the critical points of the volume functional and a natural extension of hyperbolic space by de Sitter space. They show that many of the critical points have geometric meaning (e.g. the existence of a spherical metric) in terms of geometric structures based on the extended hyperbolic space.
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