Results 31 to 40 of about 149 (127)

A universal Lipschitz extension property of Gromov hyperbolic spaces

Revista Matemática Iberoamericana, 2007
A metric space U has the universal Lipschitz extension property if for an arbitrary metric space M and every subspace S
Brudnyi, Alexander, Brudnyi, Yuri
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Non-Gromov hyperbolicity of asymptotic Teichmuller spaces

Advances in Computer Science Research, 2014
In this paper, we prove that the asymptotic Teichmuller space of Riemann surfaces of analytically infinite type with the asymptotic Teichmuller metricis not Gromov hyperbolic.
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Properly embedded least area planes in Gromov hyperbolic $3$-spaces [PDF]

Proceedings of the American Mathematical Society, 2007
We show that for any simple closed curve in the sphere at infinity of a Gromov hyperbolic 3-space with cocompact metric, there exist a properly embedded least area plane in the space spanning the given curve. This gives a positive answer to a conjecture of Gabai. Soma has already proven this conjecture earlier.
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Uniformization of intrinsic Gromov hyperbolic spaces

The purpose of this paper is to provide a uniformization procedure for Gromov hyperbolic spaces, which need not be geodesic or proper. We prove that the conformal deformation of a Gromov hyperbolic space is a bounded uniform space. Further, we show that there is a natural quasi-isometry between the Gromov boundary and the metric boundary of the ...
Allu, Vasudevarao, Jose, Alan P
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Sphericalization with its applications in Gromov hyperbolic spaces

, 2020
In this paper, we study certain applications of sphericalization in Gromov hyperbolic metric spaces. We first show that the doubling property regarding two classes of metrics on the Gromov boundary of hyperbolic spaces are coincided. Next, we obtain a characterization of unbounded Gromov hyperbolic domains via metric spaces sphericalization.
Zhou, Qingshan, Li, Yaxiang, Li, Xining
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Uniformizing Gromov hyperbolic spaces with Busemann functions

, 2020
Given a complete Gromov hyperbolic space $X$ that is roughly starlike from a point $ $ in its Gromov boundary $\partial_{G}X$, we use a Busemann function based at $ $ to construct an incomplete unbounded uniform metric space $X_{\varepsilon}$ whose boundary $\partial X_{\varepsilon}$ can be canonically identified with the Gromov boundary $\partial_ ...
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Quasihyperbolic metric and Gromov hyperbolic spaces I

arXiv admin note: text overlap with arXiv:1706.05494 by other ...
Liu, Hongjun, Xia, Ling, Yan, Shasha
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Otal-Peigné's Theorem for Gromov-hyperbolic spaces

This paper comes as an extension of a work that has been divided in two parts. The original first part corresponds to arXiv:2105.11774. The second part contained a mistake that has been corrected with a completely new strategy.
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Worm Domains are not Gromov Hyperbolic. [PDF]

J Geom Anal, 2023
Arosio L, Dall'Ara GM, Fiacchi M.
europepmc   +1 more source

Gromov hyperbolization of unbounded noncomplete spaces and Hamenstädt metric

, 2020
In this paper, we investigate Gromov hyperbolizations of unbounded locally complete and incomplete metric spaces associated with three hyperbolic type metrics: the hyperbolization metric introduced by Ibragimov, the distance ratio metric, and the quasihyperbolic metric.
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