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Sewing Homeomorphisms and Quasidisks

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Abstract

The geometry of a Jordan domain D is encoded in properties of the homeomorphism \(h:\partial {\rm D}\rightarrow \partial {\rm D}\) D induced by conformal mappings of D and D* onto the unit disk D. We illustrate here how h can be used to study quasidisks.

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References

  1. L. V. Ahlfors, Conformal Invariants, McGraw-Hill 1973.

  2. G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen. Distortion functions for plane quasiconformal mappings, Israel J. Math. 62 (1988), 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  3. —, Conformal Invariants, Inequalities, and Quasiconformal Maps, John Wiley & Sons 1997.

  4. A. Beurling and L. V. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125–142.

    Article  MathSciNet  MATH  Google Scholar 

  5. F. P. Gardiner and D. P. Sullivan, Symmetric structures on a closed curve, Amer. J. Math. 114 (1992), 683–736.

    Article  MathSciNet  MATH  Google Scholar 

  6. F. W. Gehring, Characteristic Properties of Quasidisks, Les Presses de l’Université de Montréal (1982), 1–97.

  7. F. W. Gehring, Uniform domains and the ubiquitous quasidisk, Jber. Deutsch. Math. Verein 89 (1987), 245–263.

    MathSciNet  Google Scholar 

  8. F. W. Gehring, Characterizations of quasidisks, Banach Center Publications 48 (1999), 11–41.

    MathSciNet  Google Scholar 

  9. F. W. Gehring and K. Hag, The ubiquitous quasidisk, to appear.

  10. A. Huber, Isometrische und konforme Verheftung, Comm. Math. Helv. 51 (1976), 319–331.

    Article  MATH  Google Scholar 

  11. J. G. Krzyż, Quasicircles and harmonic measure, Ann. Acad. Sci. Fenn. 12 (1987), 19–24.

    MATH  Google Scholar 

  12. J. G. Krzyż, Quasisymmetric functions and quasihomographies, Ann. Univ. M. Curie-Sklodowska 47 (1993), 90–95.

    MATH  Google Scholar 

  13. O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, Springer-Verlag, Berlin, 1987.

    Google Scholar 

  14. D. Partyka, A sewing theorem for complementary Jordan domains, Ann. Univ. M. Curie-Sklodowska 41 (1987), 99–103.

    MathSciNet  MATH  Google Scholar 

  15. A. Pfluger, Uber die Konstruktion Riemannscher Flächen durch Verheftung, J. Indian Math. Soc. 24 (1960), 260–276.

    MathSciNet  Google Scholar 

  16. J. Väisälä, Quasimöbius maps, J. d’Analyse Math. 44 (1984/85), 218–234.

    Article  Google Scholar 

  17. S. Yang, Characterizations of symmetric quasicircles, Proceedings of the 10th International Conference on Complex Analysis (2002), 188–193.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Frederick W. Gehring

  2. Institutt for matematiske fag, NTNU, 7491, Trondheim, Norway

    Kari Hag

Authors
  1. Frederick W. Gehring
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  2. Kari Hag
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Correspondence to Frederick W. Gehring.

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Dedicated to the memory of Dieter Gaier

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Gehring, F.W., Hag, K. Sewing Homeomorphisms and Quasidisks. Comput. Methods Funct. Theory 3, 143–150 (2004). https://doi.org/10.1007/BF03321031

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  • DOI: https://doi.org/10.1007/BF03321031

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