Convexity, critical points, and connectivity radius

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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.

Original languageEnglish
Pages (from-to)1279-1281
Number of pages3
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - 2020

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