Abstract
De Lellis and Topping proved an almost-Schur lemma for the closed manifolds with non-negative Ricci curvature. In this article, we study general closed manifolds and obtain a generalization of their theorem.
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Cheng X., Zhou D.: Rigidity of closed totally umbilical hypersurfaces in space forms (preprint) (2012)
Ge Y., Wang G.: A new conformal invariant on 3-dimensional manifolds. arXiv:1103.3838 (2011)
Ge Y., Wang G.: An almost Schur theorem on 4-dimensional manifolds. Proc. Amer. Math. Soc. 140, 1041–1044 (2012)
Ge Y., Wang G., Xia C.: On problems related to an inequality of De Lellis and Topping (preprint) (2011)
De Lellis C., Müller S.: Optimal rigidity estimates for nearly umbilical surfaces. J. Differential Geom. 69, 75–110 (2005)
De Lellis C., Topping P.: Almost-Schur lemma. Calc. Var. Partial Differential Equations 43 347–354 (2012). arXiv:1003.3527v2 [math.DG] 7 May 2011
Kalka M., Mann E., Yang D., Zinger A.: the exponential decay rate of the lower bound for the first Eigenvalue of compact manifolds. Internat. J. Math. (IJM) 8(3), 345–355 (1997)
Li P., Yau S.T.: Eigenvalues of a compact Riemannian manifold. AMS Proc. Symp. Pure Math. 36, 205–239 (1980)
Perez D.: On nearly umbilical hypersurfaces. Thesis (2011)
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Cheng, X. A generalization of almost-Schur lemma for closed Riemannian manifolds. Ann Glob Anal Geom 43, 153–160 (2013). https://doi.org/10.1007/s10455-012-9339-8
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DOI: https://doi.org/10.1007/s10455-012-9339-8