Pre-Schwarzian and Schwarzian derivatives of harmonic mappings

2012/10/08 by Rodrigo Hernández, Hernández, Rodrigo, María Martín +1 · 1 citation
Mathematics · #30C45 (Secondary) #30C55 (Primary) 31A05 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1210.2330

openalex publication_date 2012/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a definition of the pre-Schwarzian and the Schwarzian derivatives of any locally univalent harmonic mapping f in the complex plane without assuming any additional condition on the (second complex) dilatation ω_f of f. Using the new definition for the Schwarzian derivative of harmonic mappings, we prove analogous theorems to those by Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the univalence of harmonic mappings.

Citations

• Higher Schwarzian operators and combinatorics of the Schwarzian derivative
• The Schwarzian derivative for harmonic mappings

Cited by

• On the pre-Schwarzian and Schwarzian derivatives of log-harmonic mappings

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