Mathematical analysis demonstrates existence of at least n tangent hyperplane pairs with slice centroids on the boundary of nested convex bodies, highlighting topological methods in geometry.
Given two symmetric convex bodies L ⊆ K ⊆ Rⁿ 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 ∩ K H ∩ K belongs to ∂ L ∂ L . The theorem makes use of Lusternik-Schnirelmann category theory.
No takes yet. Share an insight, caveat, or question.
A 2026 study studied this question.
Synapse has enriched 2 closely related papers on similar clinical questions. Consider them for comparative context: