Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Su, Mengwei, Sun, Qiang, Xiong, Ge
Institutions: Tongji University, Fudan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220715082