Journal of Convex Analysis 12 (2005), No. 1, 187--196
Copyright Heldermann Verlag 2005
Geodetically Convex Sets in the Heisenberg Group
Roberto Monti
Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
Permanent Address: Università di Padova, Dipartimento di Matematica Pura e Applicata, Via Belzoni 7, 35131 Padova, Italy
monti@math.unipd.it
Matthieu Rickly
Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
matthieu.rickly@math-stat.unibe.ch
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.
[ Fulltext-pdf (316 KB)] for subscribers only.