Sharp geometric inequalities for the general $p$-affine capacity
Functional Analysis
2017-05-23 v1 Differential Geometry
Metric Geometry
Abstract
In this article, we propose the notion of the general -affine capacity and prove some basic properties for the general -affine capacity, such as affine invariance and monotonicity. The newly proposed general -affine capacity is compared with several classical geometric quantities, e.g., the volume, the -variational capacity and the -integral affine surface area. Consequently, several sharp geometric inequalities for the general -affine capacity are obtained. These inequalities extend and strengthen many well-known (affine) isoperimetric and (affine) isocapacitary inequalities.
Cite
@article{arxiv.1705.07482,
title = {Sharp geometric inequalities for the general $p$-affine capacity},
author = {Han Hong and Deping Ye},
journal= {arXiv preprint arXiv:1705.07482},
year = {2017}
}