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Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space

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arxiv 2312.16022 v2 pith:UY4WM7NM submitted 2023-12-26 math.DG gr-qc

Xiaoxiang Chai (POSTECH) , Xueyuan Wan (CQUT) This is my paper · ORCID
classification math.DGgr-qc
keywords convexrigidityparaboliccurvaturehyperbolicpolytopesprovescalar
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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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  1. Scalar curvature rigidity of parabolically convex domains in hyperbolic spaces

    math.DG 2024-11 reject novelty 6.0 of 10

    A nonzero-degree map into a parabolically convex hyperbolic domain, with scalar curvature and boundary curvature bounds, forces the domain to be hyperbolic and the boundary map to be an isometry.

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