Dihedral rigidity in hyperbolic 3-space
Xiaoxiang Chai (KIAS), Gaoming Wang
TL;DR
This paper proves a comparison theorem for polyhedra in hyperbolic 3-space with scalar curvature bounds, supporting the Gromov dihedral rigidity conjecture in this setting.
Contribution
It establishes a comparison theorem for polyhedra in hyperbolic 3-space, confirming cases of the Gromov dihedral rigidity conjecture.
Findings
Confirmation of the Gromov dihedral rigidity conjecture in certain cases
Development of a comparison theorem for polyhedra with scalar curvature bounds
Advancement in understanding rigidity phenomena in hyperbolic 3-space
Abstract
We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by . The result confirms in some cases the Gromov dihedral rigidity conjecture in hyperbolic -space.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals