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Conformal welding for domains close to a disk

Conformal welding for domains close to a disk 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Conformal welding for domains close to a disk

Analysis and Mathematical Physics , Volume 1 (3) – Jul 15, 2011

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Basel AG
Subject
Mathematics; Mathematical Methods in Physics; Analysis
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-011-0007-0
Publisher site
See Article on Publisher Site

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.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Jul 15, 2011

References