Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces

Chao Li

doi:10.3842/SIGMA.2020.099

Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces

Chao Li

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedrons enclosed by horospheres in hyperbolic manifolds, extending Gro-mov’s comparison theory to metrics with negative scalar curvature lower bounds. Our result is a localization of the positive mass theorem for asymptotically hyperbolic manifolds. We also motivate and formulate some open questions concerning related rigidity phenomenon and convergence of metrics with scalar curvature lower bounds.

Original language	English (US)
Article number	099
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	16
DOIs	https://doi.org/10.3842/SIGMA.2020.099
State	Published - 2020

Keywords

Comparison theorem
Dihedral rigidity
Hyperbolic manifolds
Scalar curvature

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2020.099

Cite this

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AB - In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedrons enclosed by horospheres in hyperbolic manifolds, extending Gro-mov’s comparison theory to metrics with negative scalar curvature lower bounds. Our result is a localization of the positive mass theorem for asymptotically hyperbolic manifolds. We also motivate and formulate some open questions concerning related rigidity phenomenon and convergence of metrics with scalar curvature lower bounds.

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Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces

Abstract

Keywords

ASJC Scopus subject areas

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