The Horofunction boundary of the Heisenberg Group: The Carnot-Carathéodory metric Journal Articles

We find the horofunction boundary of the(2n+1)(2n+1)-dimensional Heisenberg group with the Carnot-Carathéodory distance and show that it is homeomorphic to a2n2n-dimensional disk and that the Busemann points correspond to the(2n−1)(2n-1)-sphere boundary of this disk. We also show that the compactified Heisenberg group is homeomorphic to a(2n+1)(2n+1)-dimensional sphere. As an application, we find the group of isometries of the Carnot-Carathéodory distance.