Two-point distortion theorems for harmonic mappings

zbMath1207.30035arXiv1005.5333MaRDI QIDQ5893989

Peter Duren, Brad G. Osgood, Martin Chuaqui Farrú

Publication date: 8 December 2010

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.5333

zbMATH Keywords

Schwarzian derivativeunivalent functionharmonic mapping

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Geometric function theory (30C99)

Related Items (3)

Growth and distortion theorems for linearly invariant families on homogeneous unit balls in \(\mathbb C^n\) ⋮ Pluriharmonic mappings and linearly connected domains in \(\mathbb C^n\) ⋮ Two-point distortion theorems for harmonic and pluriharmonic mappings

Cites Work

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• Injectivity criteria for holomorphic curves in \(\mathbb{C}^n\)
• Univalence criteria for lifts of harmonic mappings to minimal surfaces
• Ein Verzerrungssatz für schlichte Funktionen
• Characteristic properties of Nehari functions
• The Schwarzian derivative for harmonic mappings
• The Schwarzian derivative and estimates of functions analytic in the unit disc
• Finding complete conformal metrics to extend conformal mappings
• Sharp Distortion Theorems Associated with the Schwarzian Derivative
• Simple curves in $\mathbb {R}^n$ and Ahlfors’ Schwarzian derivative
• The Schwarzian derivative and schlicht functions
• Some Criteria of Univalence

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