Dihedral Rigidity of Parabolic Polyhedrons in Hyperbolic Spaces

Chao Li

Symmetry, integrability and geometry: methods and applications, Tome 16 (2020)

Résumé

In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedrons 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 phenomenon and convergence of metrics with scalar curvature lower bounds.

Détail

Keywords: dihedral rigidity, scalar curvature, comparison theorem, hyperbolic manifolds.

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