Geodesic
Geodetically Convex Sets in the Heisenberg Group
Journal of convex analysis, Tome 12 (2005) no. 1, pp. 187-196 Cet article a éte moissonné depuis la source Heldermann Verlag

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We prove that the geodetic envelope of a subset of the Heisenberg group containing three points not lying on the same geodesic is the whole group. As a corollary, we obtain that a function on the group which is convex along geodesics must be constant. 
@article{JCA_2005_12_1_JCA_2005_12_1_a12,
     author = {R. Monti and M. Rickly},
     title = {Geodetically {Convex} {Sets} in the {Heisenberg} {Group}},
     journal = {Journal of convex analysis},
     pages = {187--196},
     year = {2005},
     volume = {12},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a12/}
}
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R. Monti; M. Rickly. Geodetically Convex Sets in the Heisenberg Group. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 187-196. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a12/