International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 22, Pages 1397-1420

On conformal dilatation in space

Christopher J. Bishop,1 Vladimir Ya. Gutlyanskiĭ,2 Olli Martio,3 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

Received 2 October 2001

Copyright © 2003 Christopher J. Bishop et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.