×

A factorization theorem for logharmonic mappings. (English) Zbl 1066.30020

A logharmonic mapping is a solution of a nonlinear elliptic partial differential equation \[ \overline{f}_{\overline{z}}= \left( a \frac {\overline{f}}{f} \right) f_z \] in a domain \(D\) of \(C\) where \(a\) is an analytic function with \(| a|< 1\) for all \(z\in D\). The aim of the paper is a sufficient and necessary condition for a nonconstant logharmonic mapping \(f\) to be factorized in the form \(f= F\circ \varphi\) where \(\varphi\) is analytic and \(F\) is univalent logharmonic.

MSC:

30C62 Quasiconformal mappings in the complex plane
PDF BibTeX XML Cite
Full Text: DOI EuDML