Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the dilatation of univalent planar harmonic mappings

Author(s): Allen Weitsman
Journal: Proc. Amer. Math. Soc. 126 (1998), 447-452.
MSC (1991): Primary 30C62, 31A05, 31A20, 49Q05
MathSciNet review: 1415341
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Abstract: It is shown that if $f$ is a univalent harmonic mapping of the unit disk onto a domain having a smooth boundary arc which is convex with respect to the domain, and if the dilatation has modulus 1 on the arc, then the arc must be a line segment.

References:

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[HS1]: W. Hengartner and G. Schober, On the boundary behavior of orientation preserving harmonic mappings, Complex Variables 5 (1986), 197-208. MR 88a:30067
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[L]: R. Laugesen, Planar harmonic maps with inner and Blaschke dilatations, to appear.

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