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Convexity, critical points, and connectivity radius


Author: Mikhail G. Katz
Journal: Proc. Amer. Math. Soc. 148 (2020), 1279-1281
MSC (2010): Primary 53C23
DOI: https://doi.org/10.1090/proc/14892
Published electronically: December 6, 2019
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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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Additional Information

Mikhail G. Katz
Affiliation: Department of Mathematics, Bar Ilan University, Ramat Gan, 5290002, Israel
Email: katzmik@macs.biu.ac.il

DOI: https://doi.org/10.1090/proc/14892
Received by editor(s): July 21, 2019
Published electronically: December 6, 2019
Communicated by: Deane Yang
Article copyright: © Copyright 2019 American Mathematical Society