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A quasiconformal dynamic property of the disk

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Abstract

It is known that every conformai embedding of the disk into the extended complex plane possesses a r2-quasiconformal extension across eachr-level line (the r2-property of a domain). We show here that this is a characteristic property of the disk: any simply connected domain which is not a disk does not admit ther 2-property.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences Department of Mathematics and Computer Science, Bar-Ilan University, 52900, Ramat Gan, Israel

    Samuel L. Krushkal

  2. Institut für Analysis Fachbereich Mathematik und Informatik, Martin-Luther UniversitÄt Halle-Wittenberg, D-06099, Halle, Germany

    Reiner Kühnau

Authors
  1. Samuel L. Krushkal
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  2. Reiner Kühnau
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Corresponding author

Correspondence to Samuel L. Krushkal.

Additional information

Supported by the RiP-program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach.

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Krushkal, S.L., Kühnau, R. A quasiconformal dynamic property of the disk. J. Anal. Math. 72, 93–103 (1997). https://doi.org/10.1007/BF02843154

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  • DOI: https://doi.org/10.1007/BF02843154

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