Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-30T20:27:29.207Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
P Koskela
Affiliation:
Department of Mathematics, University of Jyväskylä, PO Box 35, Fin-40351 Jyväskylä, Finland. E-mail: [email protected]
S Rohde
Affiliation:
Department of Mathematics, TU Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany. E-mail: [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)