FUNDAMENTAL DOMAINS FOR KLEINIAN GROUPS

1974 ◽  
pp. 31-42 ◽  
Author(s):  
A. F. Beardon
Keyword(s):  
Kleinian Groups ◽  
Fundamental Domains

scholarly journals Singular Sets of Some Kleinian Groups (II)

1967 ◽  
Vol 29 ◽  
pp. 145-162 ◽  
Author(s):  
Tohru Akaza
Keyword(s):  
Kleinian Groups ◽  
Singular Set ◽  
Fundamental Domains ◽  
Dimensional Measure ◽  
Singular Sets ◽  
Discontinuous Groups ◽  
Positive Capacity ◽  
Automorphic Functions

In the theory of automorphic functions it is important to investigate the properties of the singular sets of the properly discontinuous groups. But we seem to know nothing about the size or structure of the singular sets of Kleinian groups except the results due to Myrberg and Akaza [1], which state that the singular set has positive capacity and there exist Kleinian groups whose singular sets have positive 1-dimensional measure. In our recent paper [2], we proved the existence of Kleinian groups with fundamental domains bounded by five circles whose singular sets have positive 1-dimensional measure and presented the problem whether there exist or not such groups in the case of four circles. The purpose of this paper is to solve this problem. Here we note that, by Schottky’s condition [4], the 1-dimensional measure of the singular set is always zero in the case of three circles.

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.

Kleinian groups acting onS 3 which are extensions

1998 ◽  
Vol 3 (4) ◽  
pp. 355-374
Author(s):  
L. Potyagailo
Keyword(s):  
Kleinian Groups

Infinite ergodic theory for Kleinian groups

2005 ◽  
Vol 25 (4) ◽  
pp. 1305-1323 ◽  
Author(s):  
MANUEL STADLBAUER ◽  
BERND O. STRATMANN
Keyword(s):  
Ergodic Theory ◽  
Kleinian Groups ◽  
Infinite Ergodic Theory
Sign in / Sign up

Export Citation Format

Share Document