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 results extends to convex domains in $R^n$.
On the characterization of some classes of proximally smooth sets / Crasta, Graziano; Ilaria, Fragalà. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 22:(2016), pp. 710-727. [10.1051/cocv/2015022]
On the characterization of some classes of proximally smooth sets
CRASTA, Graziano;
2016
Abstract
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 results extends to convex domains in $R^n$.File allegati a questo prodotto
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