Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space
Differential Geometry
2024-11-18 v2 General Relativity and Quantum Cosmology
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.
Keywords
Cite
@article{arxiv.2312.16022,
title = {Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space},
author = {Xiaoxiang Chai and Xueyuan Wan},
journal= {arXiv preprint arXiv:2312.16022},
year = {2024}
}
Comments
This paper was separated into two papers with several improvements in arXiv:2407.10212 and arXiv:2408.13801. Please consider citing the two said papers instead