The Journal of Geometric Analysis

, 17:49

Univalence criteria for lifts of harmonic mappings to minimal surfaces


    • Universidad Católica de Chile
  • P. Duren
    • University of Michigan
  • B. Osgood
    • Stanford University

DOI: 10.1007/BF02922082

Cite this article as:
Chuaqui, M., Duren, P. & Osgood, B. J Geom Anal (2007) 17: 49. doi:10.1007/BF02922082


A general criterion in terms of the Schwarzian derivative is given for global univalence of the Weierstrass-Enneper lift of a planar harmonic mapping. Results on distortion and boundary regularity are also deduced. Examples are given to show that the criterion is sharp. The analysis depends on a generalized Schwarzian defined for conformai metrics and on a Schwarzian introduced by Ahlfors for curves. Convexity plays a central role.

Math Subject Classifications


Key Words and Phrases

Harmonic mappingSchwarzian derivativecurvatureminimal surface

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© Mathematica Josephina, Inc. 2007