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arXiv · 1305.3004

Some higher order isoperimetric inequalities via the method of optimal transport

Sun-Yung A. Chang·Yi Wang
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Abstract

In this paper, we establish some sharp inequalities between the volume and the integral of the $k$-th mean curvature for $k+1$-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.

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Sun-Yung A. Chang, Yi Wang. 2013-05-14. Some higher order isoperimetric inequalities via the method of optimal transport. https://arxiv.org/abs/1305.3004

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