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Conformal Metrics on the Unit Ball in Euclidean Space |
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| Authors: | Bonk, M Koskela, P Rohde, S |
| Affiliation: | Department of Mathematics, TU Braunschweig Pockelsstrasse 14, 38106 Braunschweig, Germany. E-mail: M.Bonk{at}tu-bs.de Department of Mathematics, University of Jyväskylä PO Box 35, Fin-40351 Jyväskylä, Finland. E-mail: pkoskela{at}math.jyu.fi Department of Mathematics, TU Berlin Strasse des 17. Juni 136, 10623 Berlin, Germany. E-mail: rohde{at}math.tu-berlin.de |
| Abstract: | We study densities  on the unit ball in euclidean space whichsatisfy a Harnack type inequality and a volume growth conditionfor the measure associated with . For these densities a geometrictheory can be developed which captures many features of thetheory of quasiconformal mappings. For example, we prove generalizationsof the Gehring-Hayman theorem, the radial limit theorem andfind analogues of compression and expansion phenomena on theboundary. 1991 Mathematics Subject Classification: 30C65. |
| Keywords: | weights quasiconformal mappings |
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