2024/10/30 by Puskar Mondal, Mondal, Puskar
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2410.23406
I prove a scalar curvature rigidity theorem for spheres. In particular, I prove that geodesic balls of radii strictly less than \fracπ2 in n+1~(n≥ 2) dimensional unit sphere can be rigid under smooth deformations that increase scalar curvature preserving the intrinsic geometry and the mean curvature of the boundary, and such rigidity result fails for the hemisphere. The proof of this assertion requires the notion of a real Killing connection and solution of the boundary value problem associated with its Dirac operator. The result serves as the sharpest refinement of the now-disproven Min-Oo conjecture.