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De Lellis–Topping type inequalities for smooth metric measure spaces

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Abstract

In this note we give a new Pohozaev-Schoen type identity in smooth metric measure spaces. Using this identity, we can establish an integral geometric inequality in smooth metric measure spaces with the \(m\)-Bakry-Émery Ricci curvature bounded from below, which generalizes a recent result of De Lellis and Topping (Calc Var 43:347–354, 2012).

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Acknowledgments

The author would like to thank Dr. Jeffrey S. Case for his interest and helpful conversations concerning the Pohozaev-Schoen identities. The author also thank the referee for valuable comments and suggestions that helped improve this paper.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Maritime University, Haigang Avenue 1550, Shanghai, 201306, People’s Republic of China

    Jia-Yong Wu

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  1. Jia-Yong Wu
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Correspondence to Jia-Yong Wu.

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This work is partially supported by the NSFC (11101267, 11271132), the Innovation Program of Shanghai Municipal Education Commission (13YZ087), and the Science and Technology Program of Shanghai Maritime University (20120061).

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Wu, JY. De Lellis–Topping type inequalities for smooth metric measure spaces. Geom Dedicata 169, 273–281 (2014). https://doi.org/10.1007/s10711-013-9855-0

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  • DOI: https://doi.org/10.1007/s10711-013-9855-0

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