2006/07/03 by Martin Chuaqui, Rodrigo Hernández, Chuaqui, M. +1
Mathematics · #Analytic and geometric function theory #Meromorphic and Entire Functions #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.math/0607068
We investigate the relationship between the univalence of f and of h in the decomposition f=h+g of a sense-preserving harmonic mapping defined in the unit disk \mathbbD⊂ℂ. Among other results, we determine the holomorphic univalent maps h for which there exists c>0 such that every harmonic mapping of the form f=h+g with |g'|< c|h'| is univalent. The notion of a linearly connected domain appears in our study in a relevant way.