Geodesic
On pairs of metrics invariant under a cocompact action of a group
Krat, S.1
1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 79-86 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S1079-6762-01-00097-X

Krat, S. 1

1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 
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Krat, S. On pairs of metrics invariant under a cocompact action of a group. Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 79-86. doi: 10.1090/S1079-6762-01-00097-X

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