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Conformal metrics on the unit ball in Euclideanspace

Published online by Cambridge University Press:  01 November 1998

M Bonk ,
P Koskela  and
S Rohde
M Bonk
Affiliation:
Department of Mathematics, TU Braunschweig, Pockelsstrasse 14, 38106 Braunschweig, Germany. E-mail: M.Bonk@tu-bs.de
P Koskela
Affiliation:
Department of Mathematics, University of Jyväskylä, PO Box 35, Fin-40351 Jyväskylä, Finland. E-mail: pkoskela@math.jyu.fi
S Rohde
Affiliation:
Department of Mathematics, TU Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany. E-mail: rohde@math.tu-berlin.de
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Abstract

We study densities $\rho$ on the unit ball in euclidean space which satisfy a Harnack type inequality and a volume growth condition for the measure associated with $\rho$. For these densities a geometric theory can be developed which captures many features of the theory of quasiconformal mappings. For example, we prove generalizations of the Gehring-Hayman theorem, the radial limit theorem and find analogues of compression and expansion phenomena on the boundary.

1991 Mathematics Subject Classification: 30C65.

Keywords

weightsquasiconformal mappings
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 77 , Issue 3 , November 1998 , pp. 635 - 664
Copyright
London Mathematical Society 1998

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