Centroids of sections of convex bodies and Lusternik-Schnirelmann category

Fuente: arXiv
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Autores principales: Haddad, Julian, Jiménez, C. Hugo, Villa, Rafael
Formato: Preprint
Publicado: 2025
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author Haddad, Julian
Jiménez, C. Hugo
Villa, Rafael
author_facet Haddad, Julian
Jiménez, C. Hugo
Villa, Rafael
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_22393
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Centroids of sections of convex bodies and Lusternik-Schnirelmann category
Haddad, Julian
Jiménez, C. Hugo
Villa, Rafael
Metric Geometry
Functional Analysis
Geometric Topology
(Primary) 52A40 (Secondary) Secondary: 52A38, 55M30
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.
title Centroids of sections of convex bodies and Lusternik-Schnirelmann category
topic Metric Geometry
Functional Analysis
Geometric Topology
(Primary) 52A40 (Secondary) Secondary: 52A38, 55M30
url https://arxiv.org/abs/2511.22393