Geodesic
Weak Convexity of the Distance Function
Journal of convex analysis, Tome 20 (2013) no. 1, pp. 93-106.

Voir la notice de l'article provenant de la source Heldermann Verlag

We investigate the sets which have neighborhood where the distance function from a point to the set is weakly convex. It is shown that such sets are proximally smooth. We obtain precise estimates for parameters of weak convexity via the size of the neighborhood and the constant of proximal smoothness of the set in the Hilbert space.
Classification : 49J52, 58C20, 52A07, 52A41, 52A05
Mots-clés : Distance function, uniform convexity, uniform smoothness, weak convexity, modulus of weak convexity, proximal smoothness, P-supporting condition 
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     author = {M. V. Balashov},
     title = {Weak {Convexity} of the {Distance} {Function}},
     journal = {Journal of convex analysis},
     pages = {93--106},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a5/}
}
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M. V. Balashov. Weak Convexity of the Distance Function. Journal of convex analysis, Tome 20 (2013) no. 1, pp. 93-106. http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a5/