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Inner estimate and quasiconformal harmonic maps between smooth domains

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Abstract

We prove a type of “inner estimate” for quasi-conformal diffeomorphisms, which satisfies a certain estimate concerning their Laplacian. This, in turn, implies that quasiconformal harmonic mappings between smooth domains (with respect to an approximately analytic metric), have bounded partial derivatives; in particular, these mappings are Lipschitz. We discuss harmonic mappings with respect to (a) spherical and Euclidean metrics (which are approximately analytic) (b) the metric induced by a holomorphic quadratic differential.

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Authors and Affiliations

  1. Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put B.B., 8100, Podgorica, Montenegro

    David Kalaj

  2. Faculty of Mathematics, Studentski TRG 16, University of Belgrade, 11000, Belgrade, Serbia

    Miodrag Mateljevic

Authors
  1. David Kalaj
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  2. Miodrag Mateljevic
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Correspondence to David Kalaj.

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Kalaj, D., Mateljevic, M. Inner estimate and quasiconformal harmonic maps between smooth domains. J. Anal. Math. 100, 117–132 (2006). https://doi.org/10.1007/BF02916757

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  • DOI: https://doi.org/10.1007/BF02916757

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