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Almost-Schur lemma
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Lellis, Camillo De and Topping, Peter, 1971-. (2012) Almost-Schur lemma. Calculus of Variations and Partial Differential Equations, Vol.43 (No.3-4). pp. 347-354. ISSN 0944-2669
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Official URL: http://dx.doi.org/10.1007/s00526-011-0413-z
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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Calculus of Variations and Partial Differential Equations |
| Publisher: | Springer |
| ISSN: | 0944-2669 |
| Date: | March 2012 |
| Volume: | Vol.43 |
| Number: | No.3-4 |
| Page Range: | pp. 347-354 |
| Identification Number: | 10.1007/s00526-011-0413-z |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/44211 |
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