Deformations of the hemisphere that increase scalar curvature

被引：60
作者：
Brendle, Simon [1 ]
Marques, Fernando C. [2 ]
Neves, Andre [3 ]
机构：
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
[2] IMPA, BR-22460320 Rio De Janeiro, Brazil
[3] Univ London Imperial Coll Sci Technol & Med, London SW7 2RH, England
来源：
INVENTIONES MATHEMATICAE | 2011年 / 185卷 / 01期
基金：
美国国家科学基金会;
关键词：
BLOW-UP PHENOMENA; RIGIDITY; MASS; PROOF; MANIFOLDS; SURFACES; SPIN;
D O I：
10.1007/s00222-010-0305-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
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收藏
页码：175 / 197
页数：23
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