Geodesic
On Closed Starshaped Sets
Journal of convex analysis, Tome 17 (2010) no. 2, pp. 659-671
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We present several new results on closed starshaped sets in Rd which mainly refer to the kernel and the boundary structure of such sets. In particular, we introduce so-called dispensable points which, in a certain sense, play the same role for closed starshaped sets that extreme points play for convex sets. Based on this notion we prove an analogue of the famous Krein-Milman theorem.
Classification : 52-99, 52A01, 52A30
Mots-clés : Asymptotic structure, cone, dispensable point, extreme point, kernel, Krein-Milman theorem, Minkowski's theorem, starshaped set, support cone 
@article{JCA_2010_17_2_JCA_2010_17_2_a18,
     author = {G. Hansen and H. Martini},
     title = {On {Closed} {Starshaped} {Sets}},
     journal = {Journal of convex analysis},
     pages = {659--671},
     year = {2010},
     volume = {17},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a18/}
}
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G. Hansen; H. Martini. On Closed Starshaped Sets. Journal of convex analysis, Tome 17 (2010) no. 2, pp. 659-671. http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a18/