An almost Schur theorem on 4-dimensional manifolds. (English) Zbl 1238.53026
The authors proves that the almost Schur theorem, introduced by De Lellis and Topping, is true on \(4\)-dimensional Riemannian manifolds of nonnegative scalar curvature.
Reviewer: Miroslav Doupovec (Brno)
MSC:
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
References:
| [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 \?\(_{2}\)-scalar curvature, J. Differential Geom. 84 (2010), no. 1, 45 – 86. · Zbl 1207.53049 |
| [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. · Zbl 0988.58013 · doi: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. · Zbl 0990.53035 · doi: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. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
