The local homeomorphism property of spatial quasiregular mappings with distortion close to one |
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Authors: | K Rajala |
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Institution: | 1. Department of Mathematics and Statistics, University of Jyv?skyl?, P.O. Box 35 (MaD), FIN-40014, ?, Finland
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Abstract: | We give a quantitative proof for a theorem of Martio, Rickman and V?is?l? MRV] on the rigidity of the local homeomorphism
property of spatial quasiregular mappings with distortion close to one. The proof is based on a distortion theory established
by using two main tools. First, we use a conformal invariant between sphere families and components of their preimages under
quasiregular mappings. Secondly, we use Hall’s quantitative isoperimetric inequality result H] to relate two different types
of distortion.
Received: April 2004 Revision: October 2004 Accepted: December 2004 |
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Keywords: | |
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