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An almost Schur theorem on 4-dimensional manifolds


Authors: Yuxin Ge and Guofang Wang
Journal: Proc. Amer. Math. Soc. 140 (2012), 1041-1044
MSC (2010): Primary 53C21; Secondary 58J05, 35J60
Published electronically: July 26, 2011
MathSciNet review: 2869088
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Abstract: In this short paper we prove that the almost Schur theorem, introduced by De Lellis and Topping, is true on 4-dimensional Riemannian manifolds of nonnegative scalar curvature and discuss some related problems on other dimensional manifolds.


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

  • 1. C. De Lellis and P. Topping, Almost Schur Theorem, to appear in Calc. Var. PDE, arXiv 1003.3527.
  • 2. Yuxin Ge, Chang-Shou Lin, and Guofang Wang, On the 𝜎₂-scalar curvature, J. Differential Geom. 84 (2010), no. 1, 45–86. MR 2629509
  • 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, 10.1007/s002200050721
  • 4. Jeff A. Viaclovsky, Conformal geometry, contact geometry, and the calculus of variations, Duke Math. J. 101 (2000), no. 2, 283–316. MR 1738176, 10.1215/S0012-7094-00-10127-5
  • 5. Y. Ge, G. Wang and C. Xia, On problems related to an inequality of DeLellis and Topping, preprint, 2011.
  • 6. Y. Ge and G. Wang, A new conformal invariant on 3-dimensional manifolds and its applications, arXiv 1103.3838.

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Additional Information

Yuxin Ge
Affiliation: Laboratoire d’Analyse et de Mathématiques Appliquées, CNRS UMR 8050, Départe- ment de Mathématiques, Université Paris Est-Créteil Val de Marne, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
Email: ge@univ-paris12.fr

Guofang Wang
Affiliation: Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstrasse 1, D-79104 Freiburg, Germany
Email: guofang.wang@math.uni-freiburg.de

DOI: https://doi.org/10.1090/S0002-9939-2011-11065-7
Received by editor(s): April 4, 2010
Received by editor(s) in revised form: December 21, 2010
Published electronically: July 26, 2011
Additional Notes: The second-named author is partly supported by SFB/TR71 of DFG
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.