Affine and linear invariant families of harmonic mappings

2014/05/20 by Martin Chuaqui, Rodrigo Hernández, Chuaqui, Martin +3
Mathematics · #30C55 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1405.5106

openalex publication_date 2014/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk and determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class S_H of univalent harmonic mappings can be formulated as a question about Schwarzian norm and, in particular, our result shows consistency between the conjectured order of S_H and the Schwarzian norm of the harmonic Koebe function.

Citations

• The Schwarzian derivative for harmonic mappings

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