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The local homeomorphism property of spatial quasiregular mappings with distortion close to one

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Abstract.

We give a quantitative proof for a theorem of Martio, Rickman and Väisälä [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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FIN-40014,  , Finland

    K. Rajala

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  1. K. Rajala
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Correspondence to K. Rajala.

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Received: April 2004 Revision: October 2004 Accepted: December 2004

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Rajala, K. The local homeomorphism property of spatial quasiregular mappings with distortion close to one. GAFA, Geom. funct. anal. 15, 1100–1127 (2005). https://doi.org/10.1007/s00039-005-0530-y

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  • DOI: https://doi.org/10.1007/s00039-005-0530-y

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