Results 1 to 10 of about 149 (127)
Potential Theory on Gromov Hyperbolic Spaces
Analysis and Geometry in Metric Spaces, 2022 Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona’s potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov ...
Kemper Matthias, Lohkamp Joachim
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Embeddings of Gromov Hyperbolic Spaces [PDF]
Geometric And Functional Analysis, 2000 To state the main result of the paper we start with two definitions: A metric space \(X\) has ``bounded growth at some scale'' if there are constants \(R>r>0\) and a positive integer \(N\) such that every open ball of radius \(R\) in \(X\) can be covered by \(N\) open balls of radius \(r\). A metric space \(X\) is ``roughly similar'' to a metric space \
Bonk, M., Schramm, O.
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Gromov hyperbolicity through decomposition of metrics spaces II [PDF]
Journal of Geometric Analysis, 2004 In this article we study the hyperbolicity in the Gromov sense of metric spaces. We deduce the hyperbolicity of a space from the hyperbolicity of its "building block components", which can be joined following an arbitrary scheme. These results are especially valuable since they simplify notably the topology and allow to obtain global results from local
Portilla, Ana +2 more
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Gromov hyperbolicity through decomposition of metric spaces [PDF]
Acta Mathematica Hungarica, 2004 We study the hyperbolicity of metric spaces in the Gromov sense. We deduce the hyperbolicity of a space from the hyperbolicity of its “building block components”. These results are valuable since they simplify notably the topology of the space and allow to obtain global results from local information.
Rodriguez, J. M., Touris, E.
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Gromov Hyperbolicity, John Spaces, and Quasihyperbolic Geodesics
The Journal of Geometric Analysis, 2022 We show that every quasihyperbolic geodesic in a John space admitting a roughly starlike Gromov hyperbolic quasihyperbolization is a cone arc. This result provides a new approach to the elementary metric geometry question, formulated in \cite[Question 2]{Hei89}, which has been studied by Gehring, Hag, Martio and Heinonen. As an application, we obtain a
Qingshan Zhou, Yaxiang Li, Antti Rasila
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Metric transforms yielding Gromov hyperbolic spaces [PDF]
Geometriae Dedicata, 2018 Final version, with several minor corrections and improvements.
Dragomir, George, Nicas, Andrew
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A characterization of high transitivity for groups acting on trees
Discrete Analysis, 2022 A characterization of high transitivity for groups acting on trees, Discrete Analysis 2022:8, 63 pp. Consider the group of all permutations of a countable set $X$ that leave all but a finite number of points fixed.
Pierre Fima +3 more
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The Boundary at Infinity of a Rough CAT(0) Space
Analysis and Geometry in Metric Spaces, 2014 We develop the boundary theory of rough CAT(0) spaces, a class of length spaces that contains both Gromov hyperbolic length spaces and CAT(0) spaces.
Buckley S.M., Falk K.
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Large deviations for random walks on Gromov-hyperbolic spaces
Annales Scientifiques de l École Normale Supérieure, 2023 Let $ $ be a countable group acting on a geodesic Gromov-hyperbolic metric space $X$ and $ $ a probability measure on $ $ whose support generates a non-elementary subsemigroup. Under the assumption that $ $ has a finite exponential moment, we establish large deviations results for the distance and the translation length of a random walk with ...
Boulanger, Adrien +3 more
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Analysis and Geometry in Metric Spaces, 2016 We consider a ‘contracting boundary’ of a proper geodesic metric space consisting of equivalence classes of geodesic rays that behave like geodesics in a hyperbolic space.We topologize this set via the Gromov product, in analogy to the topology of the ...
Cashen Christopher H.
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