Sharp Riesz capacity inequalities and the Pólya--Szegő conjecture

Mengwei Su, Qiang Sun, Ge Xiong

For $n\ge 2$ 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…