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

Contact details are reproduced from the original publication and may be historical.

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

R. Monti, M. Rickly. “Geodetically Convex Sets in the Heisenberg Group.” Journal of Convex Analysis 12 (2005), No. 1, 187–196.