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- W52995345 abstract "The notion of Gromov hyperbolicity was introduced by Gromov in the setting of geometric grouptheory [G1], [G2], but has played an increasing role in analysis on general metric spaces [BHK],[BS], [BBo], [BBu], and extendability of Lipschitz mappings [L].In this theory, it is often additionally assumed that the hyperbolic metric space is proper andgeodesic (meaning that closed balls are compact, and each pair of points can be joined by a pathwhose length equals the distance between the points). These additional assumptions are usefulin proofs, and valid for large classes of examples of hyperbolic spaces, for instance Cayley graphsof (nitely generated) hyperbolic groups, and certain important conformal distortions of locallycompact length metrics that push the boundary of the space to innity; see for instance [BHK, 2.8]for the case of a quasihyperbolic metric. However if the underlying metric is not locally compact,as in examples that arise in a Banach space context, then such hyperbolic conformal distortionstypically fail to be proper and geodesic (although they are always length spaces).Without these added assumptions, a few standard results for hyperbolic spaces may fail; forone such example, see [GH, 5.13]. However, Vaisala recently proved [V1] that a large part of thetheory of hyperbolic spaces goes through if we merely assume the metric is a length metric and notgeodesic or proper; Vaisala then applied this theory in a Banach space context [V2].Our paper adds to the work of [V1] by extending a characterization by Bonk of hyperbolicityin a geodesic context [B] to a length space context; see Theorem 2.1 below. Note that our versionsays a little more than Bonk's result even in a geodesic space context." @default.
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- W52995345 date "2008-01-01" @default.
- W52995345 modified "2023-09-26" @default.
- W52995345 title "Detours and Gromov hyperbolicity" @default.
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