Univalence criteria for lifts of harmonic mappings to minimal surfaces



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

30C99 31A05 53A10 

Key Words and Phrases

Harmonic mapping Schwarzian derivative curvature minimal surface 

Copyright information

© Mathematica Josephina, Inc. 2007

Authors and Affiliations

  1. 1.Universidad Católica de ChileChile
  2. 2.University of MichiganUSA
  3. 3.Stanford UniversityUSA

Personalised recommendations