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Differentiability of quasi-conformal maps on the jungle gym
Author(s):
Zsuzsanna
Gönye
Journal:
Trans. Amer. Math. Soc.
359
(2007),
19-32.
MSC (2000):
Primary 30C62, 28A78;
Secondary 30F35
Posted:
August 15, 2006
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Abstract:
We obtain a result on the quasi-conformal self-maps of jungle gyms, a divergence-type group. If the dilatation is compactly supported, then the induced map on the boundary of the covering disc  is differentiable with non-zero derivative on a set of Hausdorff dimension  . As one of the corollaries, we show that there are quasi-symmetric homeomorphisms over divergence-type groups such that for all sets  the Hausdorff dimension of  and  cannot both be less than  . This shows an important difference between finitely generated and divergence-type groups.
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Additional Information:
Zsuzsanna
Gönye
Affiliation:
Department of Mathematics, Polytechnic University, Brooklyn, New York 11201
Email:
zgonye@poly.edu
DOI:
10.1090/S0002-9947-06-04198-5
PII:
S 0002-9947(06)04198-5
Keywords:
Fuchsian group,
Kleinian group,
quasi-conformal map,
jungle gym,
Hausdorff dimension
Received by editor(s):
September 9, 2004
Posted:
August 15, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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