scholarly journals Normalizer, divergence type, and Patterson measure for discrete groups of the Gromov hyperbolic space

2020 ◽  
Vol 14 (2) ◽  
pp. 369-411
Author(s):  
Katsuhiko Matsuzaki ◽  
Yasuhiro Yabuki ◽  
Johannes Jaerisch
Keyword(s):  
Hyperbolic Space ◽  
Discrete Groups ◽  
Gromov Hyperbolic ◽  
Divergence Type

scholarly journals Uniform cantor sets as hyperbolic boundaries

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1737-1745 ◽  
Author(s):  
Yingqing Xiao ◽  
Junping Gu
Keyword(s):  
Hyperbolic Space ◽  
Cantor Set ◽  
Cantor Sets ◽  
Gromov Hyperbolic ◽  
Hyperbolic Boundary

In this paper, we prove that the Gromov hyperbolic space (?,h) which was introduced by Z. Ibragimov and J. Simanyi in [3] is an asymptotically PT??1 space and extend the methods of [3] to the case of uniform Cantor sets, show that the uniform Cantor set is isometric to the Gromov hyperbolic boundary at infinity of some asymptotically PT-1 space.

scholarly journals Hyperbolization of the limit sets of some geometric constructions

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1535-1544
Author(s):  
Zhanqi Zhang ◽  
Yingqing Xiao
Keyword(s):  
Hyperbolic Space ◽  
Geometric Constructions ◽  
Limit Sets ◽  
Fractal Sets ◽  
Fractal Set ◽  
New Class ◽  
Gromov Hyperbolic ◽  
Hyperbolic Boundary

Inspired by the construction of Sierpi?ski carpets, we introduce a new class of fractal sets. For a such fractal set K, we construct a Gromov hyperbolic space X (which is also a strongly hyperbolic space) and show that K is isometric to the Gromov hyperbolic boundary of X. Moreover, under some conditions, we show that Con(K) and X are roughly isometric, where Con(K) is the hyperbolic cone of K.

scholarly journals Bounded cohomology and totally real subspaces in complex hyperbolic geometry

2011 ◽  
Vol 32 (2) ◽  
pp. 467-478 ◽  
Author(s):  
MARC BURGER ◽  
ALESSANDRA IOZZI
Keyword(s):  
Hyperbolic Space ◽  
Hyperbolic Geometry ◽  
Isometry Group ◽  
Complex Hyperbolic Space ◽  
Discrete Groups ◽  
Connected Component ◽  
Bounded Cohomology ◽  
Finitely Generated ◽  
Complex Hyperbolic Geometry ◽  
Totally Real

AbstractWe characterize representations of finitely generated discrete groups into (the connected component of) the isometry group of a complex hyperbolic space via the pullback of the bounded Kähler class.

Topological stability and Gromov hyperbolicity

1999 ◽  
Vol 19 (1) ◽  
pp. 143-154 ◽  
Author(s):  
RAFAEL OSWALDO RUGGIERO
Keyword(s):  
Riemannian Manifold ◽  
Hyperbolic Space ◽  
Geodesic Flow ◽  
Positive Curvature ◽  
Universal Covering ◽  
Conjugate Points ◽  
Gromov Hyperbolicity ◽  
Topological Stability ◽  
Shadowing Property ◽  
Gromov Hyperbolic

We show that if the geodesic flow of a compact analytic Riemannian manifold $M$ of non-positive curvature is either $C^{k}$-topologically stable or satisfies the $\epsilon$-$C^{k}$-shadowing property for some $k > 0$ then the universal covering of $M$ is a Gromov hyperbolic space. The same holds for compact surfaces without conjugate points.

Distance Distribution between Complex Network Nodes in Hyperbolic Space

2016 ◽  
Vol 25 (3) ◽  
pp. 223-236 ◽  
Author(s):  
Gregorio Alanis-Lobato ◽  
Miguel A. Andrade-Navarro ◽  
Keyword(s):  
Complex Network ◽  
Hyperbolic Space ◽  
Distance Distribution ◽  
Network Nodes

Density of tube packings in hyperbolic space

2004 ◽  
Vol 214 (1) ◽  
pp. 127-145 ◽  
Author(s):  
Andrew Przeworski
Keyword(s):  
Hyperbolic Space

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

Sign in / Sign up

Export Citation Format

Share Document