Aspects of Quasiconformal Homogeneity
From NZJM
New Zealand Journal of Mathematics
Vol. 39, (2009), Pages 117-132
Jianhua Gong
Department of Mathematical Science
United Arab Emirates University
P.O. Box 17551
Al Ain
United Arab Emirates
Gaven Martin
Institute for Advanced Study
Massey University
Private Bag
Auckland
New Zealand
mailto:g.j.martin@massey.ac.nz
Abstract This paper studies the notion of quasiconformal homogeneity in various different settings - relative with respect to domains and ambiently. For instance we give an example of a compact set E which is homogeneous with respect to a quasiconformal family of maps of a domain containing E, but which is not quasiconformally homogeneous with respect to . We construct Cantor sets which are K--quasiconformally homogeneous for each K > 1 and explicitly identify their Hausdorff dimension, among other things.
Keywords quasiconformal, homogeneity, quasiconformal groups, Lie group.
Classification (MSC2000) Primary: 30C60.