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}
}
  • M. Katz
  • Published 6 October 2019
  • Mathematics
  • Proceedings of the American Mathematical Society
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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