Differentiability of quasi-conformal maps on the jungle gym

Autor:	Zsuzsanna Gönye
Rok vydání:	2006
Předmět:	Fuchsian group Pure mathematics Group (mathematics) Kleinian group Symmetric group Applied Mathematics General Mathematics Hausdorff dimension Mathematical analysis Boundary (topology) Differentiable function Homeomorphism Mathematics
Zdroj:	Transactions of the American Mathematical Society. 359:19-32
ISSN:	1088-6850 0002-9947
DOI:	10.1090/s0002-9947-06-04198-5
Popis:	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 D is differentiable with non-zero derivative on a set of Hausdorff dimension 1. As one of the corollaries, we show that there are quasi-symmetric homeomorphisms over divergence-type groups such that for all sets E the Hausdorff dimension of E and f(E c ) cannot both be less than 1. This shows an important difference.between finitely generated and divergence-type groups.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4115ddff2ca4e360fe578e68fc1954c4 https://doi.org/10.1090/s0002-9947-06-04198-5 Zobrazit plný text záznamu