A Rigidity Theorem for the Hemisphere

2007/11/28 by Fengbo Hang, Xiaodong Wang, Hang, Fengbo +1
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Variational Analysis #Point processes and geometric inequalities #math.DG

paper · pdf · doi:10.48550/arxiv.0711.4595

The extrinsic boundary condition is relaxed

openalex publication_date 2007/11/28 · arxiv created 2007/12/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the following rigidity theorem: For an n-dimensional compact Riemannian manifold with boundary whose Ricci curvature is bounded by n-1 from below, if its boundary is isometric to the standard sphere of dimension n-1 and totally geodesic, then the manifold is isometric to the standard hemisphere.

Related

• A note on Hang-Wang's hemisphere rigidity theorem
• Ricci and Scalar Curvature Rigidity of the Hemisphere
• Some characterizations of Riemannian manifolds endowed with a conformal vector fields
• Scalar curvature rigidity with a volume constraint
• The size of isoperimetric surfaces in 3-manifolds and a rigidity result for the upper hemisphere