Ge Xiong

activity

20242026

collaborators

3 papers

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…

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

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

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

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