Convexity, critical points, and connectivity radius
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- by Mikhail G. Katz PDF
- Proc. Amer. Math. Soc. 148 (2020), 1279-1281 Request permission
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.References
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Additional Information
- Mikhail G. Katz
- Affiliation: Department of Mathematics, Bar Ilan University, Ramat Gan, 5290002, Israel
- MR Author ID: 197211
- Email: katzmik@macs.biu.ac.il
- Received by editor(s): July 21, 2019
- Published electronically: December 6, 2019
- Communicated by: Deane Yang
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1279-1281
- MSC (2010): Primary 53C23
- DOI: https://doi.org/10.1090/proc/14892
- MathSciNet review: 4055954