On the characterization of some classes of proximally smooth sets
Dipartimento di Matematica “G. Castelnuovo”, Univ. di Roma I, P.le
A. Moro 2 – 00185
2 Dipartimento di Matematica, Politecnico, Piazza Leonardo da Vinci, 32 – 20133 Milano, Italy.
We provide a complete characterization of closed sets with empty interior and positive reach in R2. As a consequence, we characterize open bounded domains in R2 whose high ridge and cut locus agree, and hence C1 planar domains whose normal distance to the cut locus is constant along the boundary. The latter result extends to convex domains in Rn.
Mathematics Subject Classification: 26B25 / 26B05 / 53A05
Key words: Distance function / proximal smoothness / positive reach / cut locus / central set / skeleton / medial axis
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