University of Library Studies and Information Technologies

A Generalization of a Classical Geometric Extremum Problem

Let ∂ C be the boundary of a compact convex body C in Rn, n≥2, and O be an interior point of C. Every straight line l containing O cuts from C a segment [AB] with end-points on ∂ C. It is shown that if [AB] is the shortest such segment, then ∂ C is smooth at the points A and B (i...