Calculus of Variations and Geometric Measure Theory
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C. De Lellis - P. Topping

Almost Schur Lemma

created by delellis on 06 May 2011
modified on 02 Jul 2013


Published Paper

Inserted: 6 may 2011
Last Updated: 2 jul 2013

Journal: Calc. Var.
Volume: 49
Pages: 347-354
Year: 2012

For the update version and eventual errata see the webpage http:/www.math.uzh.chdelellis


Schur's lemma states that every Einstein manifold of dimension $n\geq 3$ 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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