Locally univalent harmonic mappings with linearly connected image domains. (Chinese. English summary) Zbl 1240.30110
Summary: The author studies necessary and sufficient conditions for locally univalent harmonic mappings in the unit disk with linearly connected image domains to be harmonic quasiconformal mappings and determines the parameter domain for a class of univalent harmonic mappings in the unit disk having the univalent harmonic stability property. The results improve and generalize those by M. Chuaqui and R. Hernández [J. Math. Anal. Appl. 332, No. 2, 1189–1194 (2007; Zbl 1160.30004)].
MSC:
| 30C75 | Extremal problems for conformal and quasiconformal mappings, other methods |
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
