Univalence criteria for lifts of harmonic mappings to minimal surfaces

DOI10.1007/BF02922082zbMath1211.30011arXivmath/0607063MaRDI QIDQ881444

Peter Duren, Martin Chuaqui Farrú, Brad G. Osgood

Publication date: 30 May 2007

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607063

zbMATH Keywords

Schwarzian derivativeharmonic mapping

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

Related Items (18)

Injectivity of minimal immersions and homeomorphic extensions to space ⋮ The Schwarzian derivatives of harmonic functions and univalence conditions ⋮ Quasiconformal extensions to space of Weierstrass-Enneper lifts ⋮ Nehari type theorems and uniform local univalence of harmonic mappings ⋮ Two-point distortion theorems for harmonic mappings ⋮ Schwarzian derivatives and uniform local univalence ⋮ Integral conditions on the Schwarzian for curves to be simple or unknotted ⋮ General criteria for curves to be simple ⋮ A class of Weierstrass-Enneper lifts of harmonic mappings ⋮ Pre-schwarzian and Schwarzian derivatives of harmonic mappings ⋮ An Ahlfors derivative for conformal immersions ⋮ Schwarzian derivative criteria for valence of analytic and harmonic mappings ⋮ Quasiconformal extensions of harmonic mappings ⋮ Schwarzian derivative, integral means, and the affine and linear invariant families of biharmonic mappings ⋮ Carleson measure of harmonic Schwarzian derivatives associated with a finitely generated Fuchsian group of the second kind ⋮ On Ahlfors' imaginary Schwarzian ⋮ HARMONIC MAPPING RELATED WITH THE MINIMAL SURFACE GENERATED BY ANALYTIC FUNCTIONS ⋮ Uniform domains on holomorphic curves

Cites Work

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