2023/12/26 by Xiaoxiang Chai, Xueyuan Wan, Chai, Xiaoxiang +1
Mathematics · #15A66 #52B11 #53C24 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2312.16022
openalex publication_date 2023/12/26 · openalex created_date 2023/12/29 · openalex updated_date 2026/07/28
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.