On the characterization of some classes of proximally smooth sets

DOI10.1051/COCV/2015022zbMATH Open1351.26025arXiv1305.2810OpenAlexW1976884631MaRDI QIDQ2994669

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Publication date: 3 August 2016

Published in: (Search for Journal in Brave)

Abstract: We provide a complete characterization of closed sets with empty interior and positive reach in $mathbb{R}^2$. As a consequence, we characterize open bounded domains in $mathbb{R}^2$ whose high ridge and cut locus agree, and hence $C^1$ planar domains whose normal distance to the cut locus is constant along the boundary. The latter results extends to convex domains in $mathbb{R}^n$.

Full work available at URL: https://arxiv.org/abs/1305.2810

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