Centroids of sections of convex bodies and Lusternik-Schnirelmann category
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914173324099584 |
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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 |