On the characterization of some classes of proximally smooth sets

Crasta, Graziano; Fragalà, Ilaria Fragalà

ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 710-727.

We provide a complete characterization of closed sets with empty interior and positive reach in $R^2$. As a consequence, we characterize open bounded domains in $R^2$ 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 result extends to convex domains in $R^n$.

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