Ge Xiong

activity

20242026

collaborators

5 papers

math.MG2026

The centered logarithmic Brunn--Minkowski inequality

Yude Liu, Qiang Sun, Ge Xiong

The logarithmic Brunn--Minkowski and logarithmic Minkowski inequalities are proved for convex bodies whose centroids are at the origin, with equality precisely for independent posi…

math.FA2026

Sharp inequalities for the Newtonian and logarithmic capacities

Mengwei Su, Qiang Sun, Ge Xiong

Sharp inequalities between the Riesz and logarithmic capacities of compact sets in $R^{n}$ are established, and the equality conditions are fully characterized. These result…

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…

math.MG2025

Fixed and periodic points of the intersection body operators of lower orders

Cheng Lin, Ge Xiong

For the intersection body operator of lower order $I_{i} K$ of a star body $K$ in $R^{n}$ , $i \in {1, 2, \dots, n - 2}$ , we prove that $I_{i}^{2} K = cK$ iff $K$ is an origin-symmetri…

math.MG2024

A matroid polytope approach to sharp affine isoperimetric inequalities for volume decomposition functionals

Yu-de Liu, Qiang Sun, Ge Xiong

New sharp affine isoperimetric inequalities for volume decomposition functionals $X_{2}$ and $X_{3}$ in $R^{n}$ are established. To fulfil this task, we prove the recursion…