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arXiv · 2312.16022

Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space

Xiaoxiang Chai·Xueyuan Wan
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Abstract

In odd dimensions, we prove a scalar curvature rigidity for parabolic convex polytopes in hyperbolic space enclosed by linear planes in the Poincare upper half-space model and convex with respect to the conformally related flat metric. Our method is based on spinor techniques and relies on the recent smoothing constructions of Brendle-Wang. We also prove a Llarull type rigidity for bounded smooth parabolic convex domains and a dihedral rigidity for polytopal initial data sets with dominant energy conditions.

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Xiaoxiang Chai, Xueyuan Wan. 2023-12-26. Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space. https://arxiv.org/abs/2312.16022

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