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On the local behavior of certain homeomorphisms. II

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Abstract

In the previous paper by the authors, it is shown that a sense-preserving homeomorphism, absolutely continuous on lines (ACL), under certain integral conditions on the complex dilation is conformal at a point. This result includes the Teichmüller-Wittich-Belinski theorem. In the present paper, it is shown that under weakened conditions the local behavior of such a homeomorphism is similar to that of a quasiconformal mapping. Bibliography: 2 titles.

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References

  1. M. Brakalova and J. A. Jenkins, “On the local behavior of certain homeomorphisms,”KŌdai Math. J.,17, 201–213 (1994).

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  2. B. Rodin, “The method of extremal length,”Bull. Am. Math. Soc.,80, 587–606 (1974).

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Authors
  1. Melkana Brakalova
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  2. James A. Jenkins
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Additional information

Dedicated to the 90th anniversary of G. M. Goluzin's birth.

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 11–20.

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Brakalova, M., Jenkins, J.A. On the local behavior of certain homeomorphisms. II. J Math Sci 95, 2178–2184 (1999). https://doi.org/10.1007/BF02172461

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  • DOI: https://doi.org/10.1007/BF02172461

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