Abstract

In this article, we continue our investigations of the boundary behavior of harmonic mappings. We first discuss the classical problem on the growth of radial length and obtain a sharp growth theorem of the radial length of K-quasiconformal harmonic mappings. Then we present an alternate characterization of radial John disks. In addition, we investigate the linear measure distortion and the Lipschitz continuity on K-quasiconformal harmonic mappings of the unit disk onto a radial John disk. Finally, using Pommerenke interior domains, we characterize certain differential properties of K-quasiconformal harmonic mappings.

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