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

Yu-de Liu; Qiang Sun; Ge Xiong

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

Metric Geometry 2024-05-29 v2

Authors: Yu-de Liu , Qiang Sun , Ge Xiong

Abstract

New sharp affine isoperimetric inequalities for volume decomposition functionals $X_{2}$ and $X_{3}$ in $\mathbb{R}^n$ are established. To fulfil this task, we prove the recursion formulas for volume decomposition functionals and find out the connection between the domains of these functionals and matroid polytopes. Applications of matroid theory to convex geometry are presented.

Keywords

intrinsic volumes of polytopes matroid theory convex analysis

Cite

@article{arxiv.2404.09152,
  title  = {A matroid polytope approach to sharp affine isoperimetric inequalities for volume decomposition functionals},
  author = {Yu-de Liu and Qiang Sun and Ge Xiong},
  journal= {arXiv preprint arXiv:2404.09152},
  year   = {2024}
}

Comments

In this version, we use the language of matroid theory to rewrite Section 4 in the previous version

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

Abstract

Keywords

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