Almost-Schur lemma

被引：42

作者：

De Lellis, Camillo ^{[1
]}

Topping, Peter M. ^{[2
]}

机构：

[1] Univ Zurich, Inst Math, CH-8057 Zurich, CH, Switzerland

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2012年 / 43卷 / 3-4期

关键词：

53C21; 53C24;

D O I：

10.1007/s00526-011-0413-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Schur's lemma states that every Einstein manifold of dimension n a parts per thousand yen 3 has constant scalar curvature. In this short note we ask to what extent the scalar curvature is constant if the traceless Ricci tensor is assumed to be small rather than identically zero. In particular, we provide an optimal L (2) estimate under suitable assumptions and show that these assumptions cannot be removed.

引用

页码：347 / 354

页数：8