A polyhedron comparison theorem for 3-manifolds with positive scalar curvature

• 成果类型: Article
• 署名作者: Li, Chao
• 署名单位: Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00895-0
• 发表日期: 2020
• 页码: 1-37
• 关键词: strong maximum principle; metric-measure-spaces; RICCI CURVATURE; capillary surfaces; holder continuity; 1st variation; RIGIDITY; REGULARITY; foliations; MANIFOLDS

摘要

The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collections of polyhedra with interior non-negative scalar curvature and mean convex faces, we prove the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean model, unless it is isometric to a flat polyhedron.