Convexity, critical points, and connectivity radius

@article{Katz2019ConvexityCP,
title={Convexity, critical points, and connectivity radius},
author={Mikhail G. Katz},
journal={Proceedings of the American Mathematical Society},
year={2019}
}

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.

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