Centroids of Sections of Convex Bodies and Lusternik–Schnirelmann Category
Abstract
Abstract Given two symmetric convex bodies $$L \subseteq K \subseteq \mathbb {R}^n$$ L ⊆ K ⊆ R n with L strictly convex, we prove that there exist at least n pairs of hyperplanes tangent to L , such that the center of mass of $$H \cap K$$ H ∩ K belongs to $$\partial L$$ ∂ L . The theorem makes use of Lusternik-Schnirelmann category theory.
Fields of Study & Subjects
Point processes and geometric inequalities
Homotopy and Cohomology in Algebraic Topology
Advanced Operator Algebra Research
Publication details
- Journal / source
- Journal of Geometric Analysis
- Volume
- 36
- Issue
- 10
- Publication date
- 12 August 2026
- Language
- EN