Andrea Calogero
Abstract
We define and investigate the notion of twisted convex hull for a subset of the Heisenberg group . 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 in particular, we give a characterization of their interior.
Author information
Andrea Calogero
andrea.calogero@unimib.itGiovanna Carcano
giovanna.carcano@unimib.itRita Pini
rita.pini@unimib.itReferences
- Z. M. Balogh, M. Rickly: Regularity of convex functions on Heisenberg groups, Ann. Sc. Norm. Sup. Pisa, Cl. Sci. (5), Vol. II (2003) 847–868.Google Scholar
- O. Calin, V. Mangione: Geodesics with constraints on Heisenberg manifolds, Result. Math. 44 (2003) 44–53.https://doi.org/10.1007/BF03322912Google Scholar
- A. Calogero, G. Carcano, R. Pini: Optimization on the Heisenberg group, Optimization 55 (2006) 387–403.https://doi.org/10.1080/02331930600662880Google Scholar
- D. Danielli, N. Garofalo, D. M. Nhieu: Notions of convexity in Carnot groups, Commun. Anal. Geom. 11 (2003) 263–341.https://doi.org/10.4310/CAG.2003.v11.n2.a5Google Scholar
- G. Lu, J. J. Manfredi, B. Stroffolini: Convex functions on the Heisenberg group, Calc. Var. Partial Differ. Equ. 19 (2004) 1–22.https://doi.org/10.1007/s00526-003-0190-4Google Scholar
- R. Monti, M. Rickly: Geodetically convex sets in the Heisenberg group, J. Convex Analysis 12 (2005) 187–196.https://doi.org/10.68381/jca12013Google Scholar
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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.