2024/10/28 by Xuan Yao, Yao, Xuan
Computer Science · Mathematics · Engineering · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Elasticity and Material Modeling
paper · pdf · doi:10.48550/arxiv.2410.21238
We prove a generalization of Gromov's conjecture on scalar curvature rigidity of convex polytopes to arbitrary convex Riemannian polytope type domains via harmonic spinors on convex domians with boundary condition constructed by Brendle. In particular, we prove a rigidity results on comparison of scalar curvature and scaled mean curvature on the boundary for any convex domain in Euclidean space, which is a parallel of Shi-Tam's results.