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Proceedings of the American Mathematical Society

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On the dilatation
of univalent planar harmonic mappings

Author: 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.

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Additional Information

Allen Weitsman
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Keywords: Harmonic mappings, dilatation, minimal surfaces
Received by editor(s): November 18, 1995
Received by editor(s) in revised form: May 6, 1996, and August 6, 1996
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1998 American Mathematical Society

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