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On the distortion of relative circle domain isomorphisms

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Abstract

Several qualitative properties of the conformal homeomorphisms between relative circle domains are proved. In particular, counterexamples are presented to the analog of Koebe’s 1/4-Theorem for conformai homeomorphisms between relative circle domains in simply connected domains, and for isomorphisms of disk packings.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92093, San Diego, La Jolla, CA, USA

    Zheng-Xu He

  2. Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Oded Schramm

Authors
  1. Zheng-Xu He
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  2. Oded Schramm
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Corresponding author

Correspondence to Zheng-Xu He.

Additional information

The first author is partially supported by an NSF grant. The second author holds the Sam and Ayala Zacks Professorial Chair.

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He, ZX., Schramm, O. On the distortion of relative circle domain isomorphisms. J. Anal. Math. 73, 115–131 (1997). https://doi.org/10.1007/BF02788140

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  • DOI: https://doi.org/10.1007/BF02788140

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