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Mappings of Finite Distortion of Polynomial Type

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Abstract

Suppose f:ℝn→ℝn is a mapping of K-bounded p-mean distortion for some p>n−1. We prove the equivalence of the following properties of f: the doubling condition for J(x,f) over big balls centered at the origin, the boundedness of the multiplicity function N(f,ℝn), the polynomial type of f, and the polynomial growth condition for f.

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Acknowledgements

I wish to thank my supervisor Academic Professor Pekka Koskela for many useful suggestions. I also wish to thank Academy Research Fellow Kai Rajala for many valuable discussions. Finally, I want to express my sincere gratitude to the referee whose helpful comments substantially improved the exposition.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014, Jyväskylä, Finland

    Changyu Guo

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  1. Changyu Guo
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Correspondence to Changyu Guo.

Additional information

Communicated by Marco Abate.

C.Y. Guo was partially supported by the Academy of Finland grant 131477.

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Guo, C. Mappings of Finite Distortion of Polynomial Type. J Geom Anal 24, 1052–1063 (2014). https://doi.org/10.1007/s12220-012-9363-8

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  • DOI: https://doi.org/10.1007/s12220-012-9363-8

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