Sharp geometric inequalities for the general p-affine capacity

2017/05/21 by Han Hong, Hong, Han, Deping Ye +1 · 1 citation
Mathematics · Medicine · #46E30 #46E35 #52A38 #53A15 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Pharmacological Effects of Medicinal Plants #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1705.07482

openalex publication_date 2017/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we propose the notion of the general p-affine capacity and prove some basic properties for the general p-affine capacity, such as affine invariance and monotonicity. The newly proposed general p-affine capacity is compared with several classical geometric quantities, e.g., the volume, the p-variational capacity and the p-integral affine surface area. Consequently, several sharp geometric inequalities for the general p-affine capacity are obtained. These inequalities extend and strengthen many well-known (affine) isoperimetric and (affine) isocapacitary inequalities.

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