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

Klein, Tom; Nicas, Andrew

doi:10.1090/S1088-4173-2010-00217-1

The Horofunction boundary of the Heisenberg Group: The Carnot-Carathéodory metric
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by Tom Klein and Andrew Nicas PDF

Conform. Geom. Dyn. 14 (2010), 269-295 Request permission

Abstract:

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

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