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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.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Applied Mathematics
Language:English
Date:2012
Deposited On:11 Aug 2011 13:17
Last Modified:16 Oct 2024 03:37
Publisher:Springer
ISSN:0944-2669
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00526-011-0413-z
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  • Content: Published Version
  • Language: English
  • Description: Nationallizenz 142-005

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