Geodesic
On the characterization of some classes of proximally smooth sets
Crasta, Graziano1  ; Fragalà, Ilaria Fragalà2
1 Dipartimento di Matematica “G. Castelnuovo”, Univ. di Roma I, P.le A. Moro 2 – 00185 Roma, Italy.
2 Dipartimento di Matematica, Politecnico, Piazza Leonardo da Vinci, 32 – 20133 Milano, Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 710-727

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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 .

Reçu le :
DOI : 10.1051/cocv/2015022
Classification : 26B25, 26B05, 53A05
Keywords: Distance function, proximal smoothness, positive reach, cut locus, central set, skeleton, medial axis

Crasta, Graziano 1 ; Fragalà, Ilaria Fragalà 2

1 Dipartimento di Matematica “G. Castelnuovo”, Univ. di Roma I, P.le A. Moro 2 – 00185 Roma, Italy.
2 Dipartimento di Matematica, Politecnico, Piazza Leonardo da Vinci, 32 – 20133 Milano, Italy. 
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     title = {On the characterization of some classes of proximally smooth sets},
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     pages = {710--727},
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Crasta, Graziano; Fragalà, Ilaria Fragalà. On the characterization of some classes of proximally smooth sets. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 710-727. doi: 10.1051/cocv/2015022

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