Pluriharmonic Mappings with the Convex Holomorphic Part
In 2018, Partyka et al. established several equivalent conditions for a sense-preserving locally injective harmonic mapping f=h+g¯ in the unit disk D with convex holomorphic part h to be quasiconformal in terms of the relationships of two-point distortion of h, g, and f. In this study, we first gene...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3450575 |
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| Summary: | In 2018, Partyka et al. established several equivalent conditions for a sense-preserving locally injective harmonic mapping f=h+g¯ in the unit disk D with convex holomorphic part h to be quasiconformal in terms of the relationships of two-point distortion of h, g, and f. In this study, we first generalize the above result to the case of pluriharmonic mappings fA=h+Ag¯, where h is a convex mapping in the unit ball Bn and A∈Lℂn,ℂn with A=1. Then, we establish a relationship of two-point distortion property between f and fA. |
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| ISSN: | 2314-4785 |