We define and investigate the notion of twisted convex hull for a subset of the Heisenberg group H. 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 H; in particular, we give a characterization of their interior.
Calogero, A., Carcano, G., Pini, R. (2007). Twisted convex hulls in the Heisenberg group. JOURNAL OF CONVEX ANALYSIS, 14(3), 607-619.
Twisted convex hulls in the Heisenberg group
CALOGERO, ANDREA GIOVANNI;CARCANO, GIOVANNA;PINI, RITA
2007
Abstract
We define and investigate the notion of twisted convex hull for a subset of the Heisenberg group H. 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 H; in particular, we give a characterization of their interior.
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