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Michael–Simon inequalities for \(k\)-th mean curvatures

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Abstract

This paper continues the study of Alexandrov–Fenchel inequalities for quermassintegrals for \(k\)-convex domains. It focuses on the application to the Michael–Simon type inequalities for \(k\)-curvature operators. The proof uses optimal transport maps as a tool to relate curvature quantities defined on the boundary of a domain.

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Acknowledgments

The author would like to thank Professor Sun-Yung Alice Chang for many discussions about this work. The author is also very grateful to the referee who read the manuscript very carefully and gave her helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Yi Wang

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  1. Yi Wang
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Correspondence to Yi Wang.

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Communicated by A. Malchiodi.

The research is partially supported by NSF Grant DMS-1205350.

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Wang, Y. Michael–Simon inequalities for \(k\)-th mean curvatures. Calc. Var. 51, 117–138 (2014). https://doi.org/10.1007/s00526-013-0668-7

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  • DOI: https://doi.org/10.1007/s00526-013-0668-7

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