On the Mostow rigidity theorem and measurable foliations by hyperbolic space

1982 ◽  
Vol 43 (4) ◽  
pp. 281-290 ◽  
Author(s):  
Robert J. Zimmer
Keyword(s):  
Hyperbolic Space ◽  
Rigidity Theorem ◽  
Mostow Rigidity

Smooth cocycle rigidity for expanding maps, and an application to Mostow rigidity

2002 ◽  
Vol 132 (3) ◽  
pp. 439-452 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Lie Group ◽  
Piecewise Smooth ◽  
Rigidity Theorem ◽  
Compact Lie Group ◽  
Expanding Maps ◽  
Cocycle Rigidity ◽  
Mostow Rigidity

We give a variation on the proof of Mostow's rigidity theorem, for certain hyperbolic 3-manifolds. This is based on a rigidity theorem for conjugacies between piecewise-conformal expanding Markov maps. The conjugacy rigidity theorem is deduced from a Livsic cocycle rigidity theorem that we prove for smooth, compact Lie group-valued cocycles over piecewise smooth expanding Markov maps.

scholarly journals An extension of Ratner's rigidity theorem to n-dimensional hyperbolic space

1987 ◽  
Vol 7 (1) ◽  
pp. 73-92 ◽  
Author(s):  
Livio Flaminio
Keyword(s):  
Hyperbolic Space ◽  
Negative Curvature ◽  
Rigidity Theorem ◽  
Compact Manifolds ◽  
Constant Negative Curvature

AbstractWe prove that the horospherical foliations of two compact manifolds of constant negative curvature are measurably isomorphic if and only if the two manifolds are isometric.

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.

scholarly journals Profinite rigidity for twisted Alexander polynomials

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jun Ueki
Keyword(s):  
Rigidity Theorem ◽  
Homology Groups ◽  
Alexander Polynomials ◽  
Twisted Homology ◽  
Hyperbolic Volumes

AbstractWe formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a {{\mathbb{Z}}}-cover of a 3-manifold with use of Mahler measures. We examine several examples associated to Riley’s parabolic representations of two-bridge knot groups and give a remark on hyperbolic volumes.

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ W n be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$ W ∈ W n and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$ W ∈ W are considered.

scholarly journals Multi-modal Entity Alignment in Hyperbolic Space

2021 ◽  
Author(s):  
Hao Guo ◽  
Jiuyang Tang ◽  
Weixin Zeng ◽  
Xiang Zhao ◽  
Li Liu
Keyword(s):  
Hyperbolic Space
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