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2013•arXiv (Cornell University)Open access

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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What this paper is about

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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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Isoperimetric inequality, Isoperimetric dimension, Mathematics, Regular polygon, Inequality, Curvature, Euclidean space, Order (exchange)

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