scholarly journals All finitely generated Kleinian groups of small Hausdorff dimension are classical Schottky groups

2019 ◽  
Vol 294 (3-4) ◽  
pp. 901-950
Author(s):  
Yong Hou
Keyword(s):  
Hausdorff Dimension ◽  
Kleinian Groups ◽  
Schottky Groups ◽  
Finitely Generated

scholarly journals Kleinian groups of small Hausdorff dimension are classical Schottky groups. I

2010 ◽  
Vol 14 (1) ◽  
pp. 473-519 ◽  
Author(s):  
Yong Hou
Keyword(s):  
Hausdorff Dimension ◽  
Kleinian Groups ◽  
Schottky Groups

scholarly journals Free vs. locally free Kleinian groups

2019 ◽  
Vol 2019 (746) ◽  
pp. 149-170
Author(s):  
Pekka Pankka ◽  
Juan Souto
Keyword(s):  
Hausdorff Dimension ◽  
Kleinian Group ◽  
Cantor Set ◽  
Cantor Sets ◽  
Kleinian Groups ◽  
The Other ◽  
Limit Set ◽  
Limit Sets ◽  
Other Hand

Abstract We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension < 1 are free. On the other hand we construct for any ε > 0 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < 1 + ε.

scholarly journals Schottky groups and limits of Kleinian groups

1967 ◽  
Vol 73 (1) ◽  
pp. 139-142
Author(s):  
Vicki Chuckrow
Keyword(s):  
Kleinian Groups ◽  
Schottky Groups

scholarly journals Commensurators of finitely generated nonfree Kleinian groups

2011 ◽  
Vol 11 (1) ◽  
pp. 605-624 ◽  
Author(s):  
Christopher Leininger ◽  
Darren D Long ◽  
Alan W Reid
Keyword(s):  
Kleinian Groups ◽  
Finitely Generated

scholarly journals Algebraic convergence of finitely generated Kleinian groups in all dimensions

2010 ◽  
Vol 432 (5) ◽  
pp. 1147-1151 ◽  
Author(s):  
Shihai Yang
Keyword(s):  
Kleinian Groups ◽  
Finitely Generated ◽  
Algebraic Convergence

scholarly journals On Periods of Meromorphic Eichler Integrals

1975 ◽  
Vol 57 ◽  
pp. 1-26
Author(s):  
Hiroki Sato
Keyword(s):  
Fuchsian Group ◽  
Kleinian Groups ◽  
Cohomology Groups ◽  
Finitely Generated ◽  
Eichler Integrals

In this paper we treat cohomology groups H1(G, C2q-1, M) of meromorphic Eichler integrals for a finitely generated Fuchsian group G of the first kind. According to L. V. Ahlfors [2] and L. Bers [4], H1(G, C2q-1, M) is the space of periods of meromorphic Eichler integrals for G. In the previous paper [8], we had period relations and inequalities of holomorphic Eichler integrals for a certain Kleinian groups.

scholarly journals FINITELY CONSTRAINED GROUPS OF MAXIMAL HAUSDORFF DIMENSION

2015 ◽  
Vol 100 (1) ◽  
pp. 108-123 ◽  
Author(s):  
ANDREW PENLAND ◽  
ZORAN ŠUNIĆ
Keyword(s):  
Hausdorff Dimension ◽  
Finite Type ◽  
Binary Tree ◽  
Rooted Tree ◽  
Finitely Generated ◽  
Subshift Of Finite Type ◽  
Regular Tree ◽  
Pattern Size ◽  
Tree Automorphisms ◽  
Pattern Group

We prove that if $G_{P}$ is a finitely constrained group of binary rooted tree automorphisms (a group binary tree subshift of finite type) defined by an essential pattern group $P$ of pattern size $d$, $d\geq 2$, and if $G_{P}$ has maximal Hausdorff dimension (equal to $1-1/2^{d-1}$), then $G_{P}$ is not topologically finitely generated. We describe precisely all essential pattern groups $P$ that yield finitely constrained groups with maximal Hausdorff dimension. For a given size $d$, $d\geq 2$, there are exactly $2^{d-1}$ such pattern groups and they are all maximal in the group of automorphisms of the finite rooted regular tree of depth $d$.

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