Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces

In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedra enclosed by horospheres in hyperbolic manifolds, extending Gromov's comparison theory to metrics with negative scalar curvature lower bounds. Our result is a localization of the positive mass the...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2020
Main Author: Li, Chao
Format: Article
Language:English
Published: Інститут математики НАН України 2020
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211021
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces. Chao Li. SIGMA 16 (2020), 099, 8 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedra enclosed by horospheres in hyperbolic manifolds, extending Gromov'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 phenomena and convergence of metrics with scalar curvature lower bounds.
ISSN:1815-0659