# Almost-Schur lemma

De Lellis, C; Topping, P M (2012). Almost-Schur lemma. Calculus of Variations and Partial Differential Equations, 43(3-4):347-354.

## Abstract

Schur’s lemma states that every Einstein manifold of dimension n ≥ 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.

Schur’s lemma states that every Einstein manifold of dimension n ≥ 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.

## Citations

24 citations in Web of Science®
16 citations in Scopus®

## Altmetrics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics 2012 11 Aug 2011 13:17 05 Apr 2016 14:58 Springer 0944-2669 https://doi.org/10.1007/s00526-011-0413-z http://opac.nebis.ch/F/?local_base=EBI01&con_lng=GER&func=find-b&find_code=090&request=001876023
Permanent URL: https://doi.org/10.5167/uzh-49087