Work

A Generalization of a Classical Geometric Extremum Problem

Year: 2026

Type: article

Abstract: Let \partial \,\mathcal{C} ∂ C be the boundary of a compact convex body \mathcal{C} C in \mathbb{R}^n,\, n\geq 2 R n , n ≥ 2 , and O O be an interior point of \mathcal C C . Every straight line l l containing O O cuts from \mathcal{C} C a segment [AB] [ A B ] with end-points on \partial \,\mathcal{C} ∂ C . It is shown that if [AB] [ A B ] is the shortest such segment, then \partial \,\mathcal{C} ∂ C is smooth at the points A A and B B (i.e. at both of them there is only one supporting hyperplane for \mathcal{C} C ) and, something more, the normals to the unique supporting hyperplanes at the points A A and

Source: Journal of convex analysis

DOI: 10.68381/jca34004

Authors: Petar Kenderov, Oleg Mushkarov, Nikolai Nikolov

Institutions: Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, University of Library Studies and Information Technologies

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Bulgarian National Science Fund

Award: G2703811756