OpenAlex ·
Sharp Riesz capacity inequalities and the Pólya--Szegő conjecture
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2610.04811
- Original
- Read it at the publisher
- Topics
Abstract
For $n\geq2$ and $p\in(n-2,n)$, we prove that closed balls maximize the ratio of Riesz $p$-capacity to Newtonian capacity among all compact subsets of $\mathbb{R}^n$. This resolves the classical Pólya--Szegő capacity ratio conjecture and its higher-dimensional extensions. For $n\geq4$, a sharp inequality for the ratio of Newtonian capacity to logarithmic capacity is established. All equality cases are characterized.
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