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Asymptotic Dilation of Regular Homeomorphisms

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Abstract

We study the asymptotic behavior of the ratio |f(z)| / |z| as \(z\rightarrow 0\) for mappings differentiable a.e. in the unit disc with non-degenerated Jacobian. The main tools involve the length-area functionals and angular dilatations depending on some real number p. The results are applied to homeomorphic solutions of a nonlinear Beltrami equation. The estimates are illustrated by examples.

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Acknowledgements

The first author was supported by EU FP7 IRSES program STREVCOMS, Grant No. PIRSES-2013-612669. The second and third authors were supported by the grant of the President of Ukraine for completitive projects F75/30308 of the State Fund for Fundamental Research.

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Authors and Affiliations

  1. Department of Mathematics, Holon Institute of Technology, 52 Golomb St., P.O.B. 305, Holon, 5810201, Israel

    Anatoly Golberg

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska St., Kiev-4, 01601, Ukraine

    Ruslan Salimov & Maria Stefanchuk

Authors
  1. Anatoly Golberg
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  2. Ruslan Salimov
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  3. Maria Stefanchuk
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Correspondence to Anatoly Golberg.

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Communicated by Daniel Aron Alpay.

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Golberg, A., Salimov, R. & Stefanchuk, M. Asymptotic Dilation of Regular Homeomorphisms. Complex Anal. Oper. Theory 13, 2813–2827 (2019). https://doi.org/10.1007/s11785-018-0833-2

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  • DOI: https://doi.org/10.1007/s11785-018-0833-2

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