Convexity, critical points, and connectivity radius
Differential Geometry
2020-01-09 v2
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.
Cite
@article{arxiv.1910.02432,
title = {Convexity, critical points, and connectivity radius},
author = {Mikhail G. Katz},
journal= {arXiv preprint arXiv:1910.02432},
year = {2020}
}
Comments
4 pages, published in Proceedings of the American Mathematical Society