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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.

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.

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23 citations in Web of Science®
20 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Date:2012
Deposited On:11 Aug 2011 13:17
Last Modified:07 Dec 2017 08:47
Publisher:Springer
ISSN:0944-2669
Publisher DOI:https://doi.org/10.1007/s00526-011-0413-z
Related URLs:http://opac.nebis.ch/F/?local_base=EBI01&con_lng=GER&func=find-b&find_code=090&request=001876023

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