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arXiv · 1705.07482

Sharp geometric inequalities for the general $p$-affine capacity

Han Hong·Deping Ye
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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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Han Hong, Deping Ye. 2017-05-21. Sharp geometric inequalities for the general $p$-affine capacity. https://arxiv.org/abs/1705.07482

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