Abstract
We obtain some De Lellis-Topping type inequalities on the smooth metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 2013, 43: 153-160].
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Cheng X. A generalization of almost-Schur lemma for closed Riemannian manifolds. Ann Global Anal Geom, 2013, 43: 153–160
Chow B, Lu P, Ni L. Hamilton’s Ricci Flow. Grad Stud Math, Vol 77. Beijing/Providence: Science Press/Amer Math Soc, 2006
De Lellis C, Topping P M. Almost-Schur lemma. Calc Var Partial Differential Equations, 2012, 43: 347–354
Ge Y X, Wang G F. An almost Schur theorem on 4-dimensional manifolds. Proc Amer Math Soc, 2012, 140: 1041–1044
Ge Y X, Wang G F. A new conformal invariant on 3-dimensional manifolds. Adv Math, 2013, 249: 131–160
Pohozaev S. On the eigenfunctions of the equation Δu+λf(u) = 0: Soviet Math Dokl, 1965, 6: 1408–1411
Schoen R. The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation. Comm Pure Appl Math, 1988, 41: 317–392
Wu J Y. De Lellis-Topping type inequalities for smooth metric measure spaces. Geom Dedicata, 2014, 169: 273–281
Acknowledgements
The authors would like to thank the referees for useful suggestions. This work was supported in part by the National Natural Science Foundation of China (Grant No. 11301017), the Research Fund for the Doctoral Program of Higher Education of China, and the Fundamental Research Funds for the Central Universities.
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Meng, M., Zhang, S. De Lellis-Topping type inequalities on smooth metric measure spaces. Front. Math. China 13, 147–160 (2018). https://doi.org/10.1007/s11464-017-0670-z
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DOI: https://doi.org/10.1007/s11464-017-0670-z