Ge Xiong

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20242026

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math.FA2026

Sharp Riesz capacity inequalities and the Pólya--Szegő conjecture

Mengwei Su, Qiang Sun, Ge Xiong

For $n \geq 2$ 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 $R^{n}$ . This resolves…

math.FA2026

An affirmative solution to the generalized Busemann--Petty problem with subspace dimensions $2$ and $3$

Cheng Lin, Yu-De Liu, Ge Xiong

The generalized Busemann--Petty problem asks whether origin-symmetric convex bodies in $R^{n}$ having larger volume of all $m$ -dimensional sections necessarily have larger v…

Sharp Riesz capacity inequalities and the Pólya--Szegő conjecture

An affirmative solution to the generalized Busemann--Petty problem with subspace dimensions 2 and 3

An affirmative solution to the generalized Busemann--Petty problem with subspace dimensions $2$ and $3$