Sphericalizations and applications in Gromov hyperbolic spaces

2021 ◽  
pp. 125948
Author(s):  
Qingshan Zhou ◽  
Yaxiang Li ◽  
Xining Li
Keyword(s):  
Hyperbolic Spaces ◽  
Gromov Hyperbolic

scholarly journals FREELY INDECOMPOSABLE GROUPS ACTING ON HYPERBOLIC SPACES

2004 ◽  
Vol 14 (02) ◽  
pp. 115-171 ◽  
Author(s):  
ILYA KAPOVICH ◽  
RICHARD WEIDMANN
Keyword(s):  
Hyperbolic Group ◽  
Conjugacy Classes ◽  
Hyperbolic Spaces ◽  
Gromov Hyperbolic ◽  
Torsion Free

We obtain a number of finiteness results for groups acting on Gromov-hyperbolic spaces. In particular we show that a torsion-free locally quasiconvex hyperbolic group has only finitely many conjugacy classes of n-generated one-ended subgroups.

scholarly journals Hyperbolic Unfoldings of Minimal Hypersurfaces

2018 ◽  
Vol 6 (1) ◽  
pp. 96-128 ◽  
Author(s):  
Joachim Lohkamp
Keyword(s):  
Point Of View ◽  
Hyperbolic Spaces ◽  
Intrinsic Geometry ◽  
Minimal Hypersurfaces ◽  
Bounded Geometry ◽  
New Concepts ◽  
Gromov Hyperbolic ◽  
Area Minimizing ◽  
Conformal Deformations ◽  
Gromov Boundary

Abstract We study the intrinsic geometry of area minimizing hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. Namely, for any such hypersurface H we define and construct a so-called S-structure. This new and natural concept reveals some unexpected geometric and analytic properties of H and its singularity set Ʃ. Moreover, it can be used to prove the existence of hyperbolic unfoldings of H\Ʃ. These are canonical conformal deformations of H\Ʃ into complete Gromov hyperbolic spaces of bounded geometry with Gromov boundary homeomorphic to Ʃ. These new concepts and results naturally extend to the larger class of almost minimizers.

scholarly journals Rough isometry between Gromov hyperbolic spaces and uniformization

2021 ◽  
Vol 46 (1) ◽  
pp. 449-464
Author(s):  
Jeff Lindquist ◽  
Nageswari Shanmugalingam
Keyword(s):  
Hyperbolic Spaces ◽  
Gromov Hyperbolic ◽  
Rough Isometry

INFINITE WORDS AND CONFLUENT REWRITING SYSTEMS: ENDOMORPHISM EXTENSIONS

2009 ◽  
Vol 19 (04) ◽  
pp. 443-490 ◽  
Author(s):  
JULIEN CASSAIGNE ◽  
PEDRO V. SILVA
Keyword(s):  
Existence And Uniqueness ◽  
Hyperbolic Spaces ◽  
Topological Structures ◽  
Infinite Words ◽  
Rewriting Systems ◽  
Rewriting System ◽  
Gromov Hyperbolic ◽  
Characterization Theorems

Infinite words over a finite special confluent rewriting system R are considered and endowed with natural algebraic and topological structures. Their geometric significance is explored in the context of Gromov hyperbolic spaces. Given an endomorphism φ of the monoid generated by R, existence and uniqueness of several types of extensions of φ to infinite words (endomorphism extensions, weak endomorphism extensions, continuous extensions) are discussed. Characterization theorems and positive decidability results are proved for most cases.

scholarly journals Properties of sets of isometries of Gromov hyperbolic spaces

2018 ◽  
Vol 12 (3) ◽  
pp. 889-910 ◽  
Author(s):  
Eduardo Oregón-Reyes
Keyword(s):  
Hyperbolic Spaces ◽  
Gromov Hyperbolic

scholarly journals Non-amenability and visual Gromov hyperbolic spaces

2017 ◽  
Vol 11 (2) ◽  
pp. 685-704
Author(s):  
Juhani Koivisto
Keyword(s):  
Hyperbolic Spaces ◽  
Gromov Hyperbolic
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