Computational Methods and Function Theory 7 (2007), No. 2, 527--541
Copyright Heldermann Verlag 2007
István Prause
istvan.prause@helsinki.fi , University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, FIN-00014 University of Helsinki, Finland.
We investigate flatness properties of K-quasiconformal spheres in the Euclidean n-dimensional space with the emphasis on the case when K is close to 1. These also lead to bounds for their Hausdorff dimension showing that K-quasispheres have much smaller dimension than K-quasiconformal images of general (n-1)-dimensional sets (K → 1). The corresponding result in the plane is well-known.
Keywords: Quasiconformal spheres, uniform flatness, Hausdorff dimension.
MSC 2000: 30C65.
[FullText-pdf (300 K)] [FullText-ps (488 K)]