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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Boundary at infinity of symmetric rank one spaces


Authors: S. Buyalo and A. Kuznetsov
Translated by: the authors
Original publication: Algebra i Analiz, tom 21 (2009), nomer 5.
Journal: St. Petersburg Math. J. 21 (2010), 681-691
MSC (2010): Primary 53C23
DOI: https://doi.org/10.1090/S1061-0022-2010-01111-7
Published electronically: July 14, 2010
MathSciNet review: 2604560
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the canonical Carnot-Carathéodory spherical and horospherical metrics, which are defined on the boundary at infinity of every rank one symmetric space of noncompact type, are visual; i.e., they are bi-Lipschitz equivalent with universal bi-Lipschitz constants to the inverse exponent of Gromov products based in the space and on the boundary at infinity respectively.


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Additional Information

S. Buyalo
Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Fontanka 27, St. Petersburg 191023, Russia
Email: sbuyalo@pdmi.ras.ru

A. Kuznetsov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii Prospekt 28, Staryi Petergof, St. Petersburg 198504, Russia
Email: kasheftin@gmail.com

DOI: https://doi.org/10.1090/S1061-0022-2010-01111-7
Keywords: Carnot–Carathéodory spherical metric, Carnot–Carathédory horospherical metric, visual metric, Gromov product
Received by editor(s): May 20, 2009
Published electronically: July 14, 2010
Additional Notes: Supported by RFBR (grant no. 08-01-00079a)
Article copyright: © Copyright 2010 American Mathematical Society