Embeddings of Gromov Hyperbolic Spaces

By M. Bonk, Oded Schramm. 2000

375 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a10ceedfe2dcaecac4f6d51c13d1bf71a0822271

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Hyperbolic groups have finite asymptotic dimension (2005, neutral): “Our proof is related to those of the finite-dimensionality of the Gromov boundary of a hyperbolic group given in [2] and [1].”
Bilipschitz Embeddings of Metric Spaces into Space Forms (2001, background): “A recent result due to M. Bonk and O. Schramm [ BoS ], restated in Theorem 6.1, provides quasi-isometric embeddings of Gromov hyperbolic spaces into real hyperbolic spaces.”
Hyperbolicity, CAT(−1)-spaces and the Ptolemy inequality (2006, background): “Remark 3 Actually in [ 3 ] it was proven more explicitly that for every positive λ 3 ]).”
Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains (2000, methodology): “[ BS ], Sec. 7) that r is a metric on Con(Z) such that (Con(Z);r) is Gromov hyperbolic.”
Boundaries of hyperbolic groups (2002, methodology): “] states the above theorem for spaces more general than Cayley graphs of hyperbolic groups. Therefore some additional assumptions on the space are present in his statement. Later M.Bonk and O.Schramm [25] showed that those additional assumptions are not needed if instead of quasiconformalmapsbetween”
Embedding of hyperbolic groups into products of binary trees (2007, background): “Any Cayley graph of a hyperbolic group is a visual, cocompact hyperbolic geodesic space and its boundary at infinity is doubling with respect to any visual metric (compare [ BoS , Theorem 9.2]; we remark here that in [BoS] the doubling condition occurs in the equivalent form of “having finite Assoua”
Uniformization of Sierpiński carpets in the plane (2010, background): “Moreover, the space (∂∞G, d) is doubling (see [10, Theorem 9.2] and the remarks after this theorem; note that the proof of [ 10, Theorem 9.2 ] contains some inaccuracies; they can easily be corrected).”
Dimensions of locally and asymptotically self-similar spaces (2005, background): “Recall that a metric space X has bounded growth at some scale, if for some constants r, R with R > r > 0, and N ∈ N every ball of radius R in X can be covered by N balls of radius r, see [ BoS ].”
Harmonicity of Quasiconformal Measures and Poisson Boundaries of Hyperbolic Spaces (2004, neutral): “4δ . Moreover, we have Proposition 1.10 (6.2 of [ BS00 ]).”