Strong hyperbolicity
Strong hyperbolicity
We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyperbolic spaces that are metrically well-behaved at infinity, and, under weak geodesic assumptions, they are strongly bolic as well. We show that CAT(?1) spaces are strongly hyperbolic. On the way, we determine the best constant of hyperbolicity for the standard hyperbolic plane H2. We also show that the Green metric defined by a random walk on a hyperbolic group is strongly hyperbolic. A measure-theoretic consequence at the boundary is that the harmonic measure defined by a random walk is a visual Hausdorff measure
951-964
Nica, Bogdan
2d1028a6-d459-4fc3-9fa3-c06105074c13
Spakula, Jan
c43164e4-36a7-4372-9ce2-9bfbba775d77
15 November 2016
Nica, Bogdan
2d1028a6-d459-4fc3-9fa3-c06105074c13
Spakula, Jan
c43164e4-36a7-4372-9ce2-9bfbba775d77
Nica, Bogdan and Spakula, Jan
(2016)
Strong hyperbolicity.
Groups, Geometry and Dynamics, 10 (3), .
(doi:10.4171/GGD/372).
Abstract
We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyperbolic spaces that are metrically well-behaved at infinity, and, under weak geodesic assumptions, they are strongly bolic as well. We show that CAT(?1) spaces are strongly hyperbolic. On the way, we determine the best constant of hyperbolicity for the standard hyperbolic plane H2. We also show that the Green metric defined by a random walk on a hyperbolic group is strongly hyperbolic. A measure-theoretic consequence at the boundary is that the harmonic measure defined by a random walk is a visual Hausdorff measure
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Accepted/In Press date: 20 July 2015
e-pub ahead of print date: 16 September 2016
Published date: 15 November 2016
Organisations:
Pure Mathematics
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Local EPrints ID: 381626
URI: http://eprints.soton.ac.uk/id/eprint/381626
ISSN: 1661-7207
PURE UUID: 5f8267cc-9983-4ee4-81ef-cf99105f3cb7
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Date deposited: 09 Oct 2015 11:06
Last modified: 15 Mar 2024 03:48
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Author:
Bogdan Nica
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