Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C62, 31A05, 31A20, 49Q05

Retrieve articles in all journals with MSC (1991): 30C62, 31A05, 31A20, 49Q05


Additional Information

Allen Weitsman
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: weits@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04076-3
PII: S 0002-9939(98)04076-3
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