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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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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Additional Information
  • Tom Klein
  • Affiliation: 325 Island Drive, Apt 6, Madison, Wisconsin 53705
  • Email:
  • Andrew Nicas
  • Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
  • MR Author ID: 131000
  • Email:
  • Received by editor(s): February 26, 2010
  • Published electronically: November 17, 2010
  • Additional Notes: The second author was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 14 (2010), 269-295
  • MSC (2010): Primary 20F65, 22E25, 53C23, 53C70
  • DOI:
  • MathSciNet review: 2738530