Journal of convex analysis, Tome 12 (2005) no. 1, pp. 187-196
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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/
@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/}
}
TY - JOUR
AU - R. Monti
AU - M. Rickly
TI - Geodetically Convex Sets in the Heisenberg Group
JO - Journal of convex analysis
PY - 2005
SP - 187
EP - 196
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a12/
ID - JCA_2005_12_1_JCA_2005_12_1_a12
ER -
%0 Journal Article
%A R. Monti
%A M. Rickly
%T Geodetically Convex Sets in the Heisenberg Group
%J Journal of convex analysis
%D 2005
%P 187-196
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a12/
%F JCA_2005_12_1_JCA_2005_12_1_a12
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.
