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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An almost Schur theorem on 4-dimensional manifolds
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by Yuxin Ge and Guofang Wang PDF
Proc. Amer. Math. Soc. 140 (2012), 1041-1044 Request permission

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
  • C. De Lellis and P. Topping, Almost Schur Theorem, to appear in Calc. Var. PDE, arXiv 1003.3527.
  • Yuxin Ge, Chang-Shou Lin, and Guofang Wang, On the $\sigma _2$-scalar curvature, J. Differential Geom. 84 (2010), no. 1, 45–86. MR 2629509
  • 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
  • Jeff A. Viaclovsky, Conformal geometry, contact geometry, and the calculus of variations, Duke Math. J. 101 (2000), no. 2, 283–316. MR 1738176, DOI 10.1215/S0012-7094-00-10127-5
  • Y. Ge, G. Wang and C. Xia, On problems related to an inequality of DeLellis and Topping, preprint, 2011.
  • 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
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1041-1044
  • MSC (2010): Primary 53C21; Secondary 58J05, 35J60
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11065-7
  • MathSciNet review: 2869088