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

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arxiv 2404.09152 v2 pith:M5DISNTL submitted 2024-04-14 math.MG

Yu-de Liu , Qiang Sun , Ge Xiong This is my paper · ORCID
classification math.MG
keywords functionalsdecompositionmatroidvolumeaffineinequalitiesisoperimetricsharp
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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.

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  1. On polynomial inequalities for cone-volumes of polytopes

    math.MG 2025-06 conditional novelty 6.0 of 10

    For any finite set of unit normals positively spanning R^n, the cone-volume set C_cv(U) is a path-connected semialgebraic set, and it equals the scaled matroid base polytope only for centrally symmetric parallelepipeds.

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