Twisted Convex Hulls in the Heisenberg Group

We define and investigate the notion of twisted convex hull for a subset of the Heisenberg group $\mathbb{H}$. 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 $\mathbb{H}$ in particular, we give a characterization of their interior.