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arXiv · 1910.02432

Convexity, critical points, and connectivity radius

Mikhail G. Katz
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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.

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Mikhail G. Katz. 2019-10-06. Convexity, critical points, and connectivity radius. https://doi.org/10.1090/proc/14892

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