International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 22, Pages 1397-1420
doi:10.1155/S0161171203110034
On conformal dilatation in space
Christopher J. Bishop1
, Vladimir Ya. Gutlyanskiĭ2
, Olli Martio3
and Matti Vuorinen3
1Department of Mathematics, SUNY at Stony Brook, Stony Brook 11794-3651, NY, USA
2Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 74 Roze Luxemburg Street, Donetsk 83114, Ukraine
3Department of Mathematics, University of Helsinki, P.O. Box 4 (Yliopistonkatu 5), FIN-00014, Finland
Abstract
We study the conformality problems associated with quasiregular mappings in space. Our approach is based on the concept of the infinitesimal space and some new Grötzsch-Teichmüller type modulus estimates that are expressed in terms of the mean value of the dilatation coefficients.