Deformations of the hemisphere that increase scalar curvature

• 成果类型: Article
• 署名作者: Brendle, Simon; Marques, Fernando C.; Neves, Andre
• 署名单位: Stanford University; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Imperial College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0305-4
• 发表日期: 2011
• 页码: 175-197
• 关键词: blow-up phenomena; RIGIDITY; mass; PROOF; MANIFOLDS; SURFACES; spin

摘要

Consider a compact Riemannian manifold M of dimension n whose boundary a,M is totally geodesic and is isometric to the standard sphere S (n-1). A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n-1), then M is isometric to the hemisphere S-+(n) equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo's Conjecture in dimension n >= 3.