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Conformal welding for domains close to a disk

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Abstract

We deduce variational formulae for domains close to a disk which generalize mappings from the unit disk and from the exterior of the unit disk onto a circular digon. These results lead to the asymptotic conformal welding for such domains. Besides we deduce the asymptotic conformal welding for circular quadrangles with inner angles απ. The by-product of the main consideration is a contribution to the Kufarev type examples in the Löwner theory. The mapping from the unit disk onto a circular digon symmetric with respect to the real axis satisfies the Löwner type equation though it is not a slit mapping.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Saratov State University, Saratov, 410012, Russia

    Dmitri Prokhorov

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  1. Dmitri Prokhorov
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Correspondence to Dmitri Prokhorov.

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D. Prokhorov’s research was partially supported by SS (Russia) 4283.2010.11.

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Prokhorov, D. Conformal welding for domains close to a disk. Anal.Math.Phys. 1, 101–114 (2011). https://doi.org/10.1007/s13324-011-0007-0

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  • DOI: https://doi.org/10.1007/s13324-011-0007-0

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