A note on the almost-Schur lemma on $4$-dimensional Riemannian closed manifolds
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- by Ezequiel R. Barbosa PDF
- Proc. Amer. Math. Soc. 140 (2012), 4319-4322 Request permission
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
- Y. Ge, G. Wang, An almost Schur Theorem on $4$-dimensional manifolds, Proc. Amer. Math. Soc. 140 (2012), pp. 1041–1044.
- C. De Lellis, P. Topping, Almost-Schur Lemma, to appear in Calc. Var. and PDE.
- 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, DOI 10.1007/s002200050721
- Morio Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry 6 (1971/72), 247–258. MR 303464
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
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 4319-4322
- MSC (2010): Primary 53C25
- DOI: https://doi.org/10.1090/S0002-9939-2012-11255-9
- MathSciNet review: 2957222