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arXiv · 2511.22393

Centroids of sections of convex bodies and Lusternik-Schnirelmann category

Julian Haddad·C. Hugo Jiménez·Rafael Villa
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Abstract

Given two symmetric convex bodies $L \subseteq K \subseteq \R^n$ with $L$ strictly convex, we prove that there exist at least $n$ hyperplanes $H$ tangent to $L$, such that the center of mass of $H \cap K$ belongs to $\partial L$. The theorem makes use of Lusternik-Schnirelmann category theory.

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Julian Haddad, C. Hugo Jiménez, Rafael Villa. 2025-11-27. Centroids of sections of convex bodies and Lusternik-Schnirelmann category. https://arxiv.org/abs/2511.22393

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