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On the Boundary Behavior of Conformal Maps*)

Published online by Cambridge University Press:  22 January 2016

S.E. Warschawski
S.E. Warschawski*
Affiliation:
University of California, San Diego, La Jolla, California, U.S.A.
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Suppose Ω is a simply connected domain which is mapped conformally onto a disk. A much studied problem is the behavior of the mapping function at an accessible boundary point P of Ω, in particular the question, under what conditions the map is ‘ “conformai” at such a point (a) in the sense that angles are preserved as P is approached from Ω (“semi-conformality” at P) and (b) the dilatation at P is finite and positive. In his fundamental paper [8] in 1936, A. Ostrowski established a necessary and sufficient condition (depending on the geometry of the domain only) for the validity of the first property which subsumes all previous results and establishes a definitive solution of this problem.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 83 - 101
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

Footnotes

*)

The preparation of this paper was sponsored (in part) by the Office of Naval Research under contract Nonr-2216(28) (NR-043-332) with the University of California.

References

Bibliographie

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