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The Horofunction boundary of the Heisenberg Group: The Carnot-Carathéodory metric
Author(s):
Tom
Klein;
Andrew
Nicas
Journal:
Conform. Geom. Dyn.
14
(2010),
269-295.
MSC (2010):
Primary 20F65, 22E25, 53C23, 53C70
Posted:
November 17, 2010
MathSciNet review:
2738530
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Abstract:
We find the horofunction boundary of the  -dimensional Heisenberg group with the Carnot-Carathéodory distance and show that it is homeomorphic to a  -dimensional disk and that the Busemann points correspond to the  -sphere boundary of this disk. We also show that the compactified Heisenberg group is homeomorphic to a  -dimensional sphere. As an application, we find the group of isometries of the Carnot-Carathéodory distance.
References:
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Additional Information:
Tom
Klein
Affiliation:
325 Island Drive, Apt 6, Madison, Wisconsin 53705
Email:
klein@math.binghamton.edu
Andrew
Nicas
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Email:
nicas@mcmaster.ca
DOI:
10.1090/S1088-4173-2010-00217-1
PII:
S 1088-4173(2010)00217-1
Keywords:
Heisenberg group,
Carnot-Carathéodory distance,
horofunction boundary,
Busemann points,
isometries
Received by editor(s):
February 26, 2010
Posted:
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 of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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