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On pairs of metrics invariant under a cocompact action of a group

Author: S. A. Krat
Journal: Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 79-86
MSC (2000): Primary 51K05; Secondary 53C99
Published electronically: September 28, 2001
MathSciNet review: 1856889
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Abstract: Consider two intrinsic metrics invariant under the same cocompact action of an abelian group. Assume that the ratio of the distances tends to one as the distances grow to infinity. Then it is known (due to D. Burago) that the difference between the metric functions is uniformly bounded. We will prove an analog of this result for hyperbolic groups, as well as a partial generalization of this result for the Heisenberg group: a word metric on the Heisenberg group lies within bounded GH distance from its asymptotic cone.

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Additional Information

S. A. Krat
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Keywords: Metric space, group action
Received by editor(s): February 16, 2001
Published electronically: September 28, 2001
Communicated by: Richard Schoen
Article copyright: © Copyright 2001 American Mathematical Society