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arXiv · 1305.2810

On the characterization of some classes of proximally smooth sets

Graziano Crasta·Ilaria Fragalà
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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 $\mathbb{R}^n$.

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Graziano Crasta, Ilaria Fragalà. 2013-05-13. On the characterization of some classes of proximally smooth sets. https://doi.org/10.1051/cocv%2F2015022

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