paper

Convexity, critical points, and connectivity radius

arXiv:1910.02432 · doi:10.1090/proc/14892

Abstract

We study the level sets of the distance function from a boundary point of a convex set in Euclidean space. We provide a lower bound for the range of connectivity of the level sets, in terms of the critical points of the distance function in the sense of Grove-Shiohama-Gromov-Cheeger.

4 pages, published in Proceedings of the American Mathematical Society

Convexity, critical points, and connectivity radius · wovepaper