Geodesic
Twisted Convex Hulls in the Heisenberg Group
Journal of convex analysis, Tome 14 (2007) no. 3, pp. 607-619 Cet article a éte moissonné depuis la source Heldermann Verlag

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We define and investigate the notion of twisted convex hull for a subset of the Heisenberg group H. We show that, while the twisted convex hull of two points is always a bounded set, the twisted convex hull of n > 2 points is, in general, an unbounded prism, with edges parallel to the t axis. These results shed some light on the twisted convex subsets of H in particular, we give a characterization of their interior.
Classification : 52A01, 53C17, 22E25
Mots-clés : Heisenberg group, twisted convex combination, twisted convex hull, horizontal planes 
@article{JCA_2007_14_3_JCA_2007_14_3_a7,
     author = {A. Calogero and G. Carcano and R. Pini},
     title = {Twisted {Convex} {Hulls} in the {Heisenberg} {Group}},
     journal = {Journal of convex analysis},
     pages = {607--619},
     year = {2007},
     volume = {14},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a7/}
}
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A. Calogero; G. Carcano; R. Pini. Twisted Convex Hulls in the Heisenberg Group. Journal of convex analysis, Tome 14 (2007) no. 3, pp. 607-619. http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a7/