Ge Xiong

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20242026

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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…