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- W3037230926 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. 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." @default.
- W3037230926 created "2020-07-02" @default.
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- W3037230926 date "2016-01-01" @default.
- W3037230926 modified "2023-09-24" @default.
- W3037230926 title "Strong hyperbolicity" @default.
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- W3037230926 doi "https://doi.org/10.4171/ggd/372" @default.
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