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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the almost-Schur lemma on $ 4$-dimensional Riemannian closed manifolds


Author: Ezequiel R. Barbosa
Journal: Proc. Amer. Math. Soc. 140 (2012), 4319-4322
MSC (2010): Primary 53C25
Published electronically: March 29, 2012
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Abstract: In this short paper, we prove a type of the almost-Schur lemma, introduced by De Lellis-Topping, on 4-dimensional Riemannian closed manifolds assuming no conditions on the Ricci tensor or the scalar curvature.


References [Enhancements On Off] (What's this?)

  • 1. Y. Ge, G. Wang, An almost Schur Theorem on $ 4$-dimensional manifolds, Proc. Amer. Math. Soc. 140 (2012), pp. 1041-1044.
  • 2. C. De Lellis, P. Topping, Almost-Schur Lemma, to appear in Calc. Var. and PDE.
  • 3. Matthew J. Gursky, The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE, Comm. Math. Phys. 207 (1999), no. 1, 131–143. MR 1724863 (2000k:58029), http://dx.doi.org/10.1007/s002200050721
  • 4. Morio Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry 6 (1971/72), 247–258. MR 0303464 (46 #2601)

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Additional Information

Ezequiel R. Barbosa
Affiliation: Department of Mathematics, ICEx, Universidade Federal de Minas Gerais, C.P. 702, Belo Horizonte, MG, CEP 30161-970, Brazil
Email: ezequiel@mat.ufmg.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11255-9
PII: S 0002-9939(2012)11255-9
Keywords: Einstein manifold, Schur’s Theorem, 4-dimensional manifold.
Received by editor(s): October 13, 2010
Received by editor(s) in revised form: April 19, 2011, and May 13, 2011
Published electronically: March 29, 2012
Additional Notes: The author was partially supported by CNPq-Brazil
Communicated by: Michael Wolf
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.