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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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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| author | Ma Lihua See Keong Lee |
| author_facet | Ma Lihua See Keong Lee |
| author_sort | Ma Lihua |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8accb09dd56b4687bbf9148d89cb0bac |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
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| series | Journal of Mathematics |
| spelling | doaj-art-8accb09dd56b4687bbf9148d89cb0bac2025-02-03T05:57:38ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3450575Pluriharmonic Mappings with the Convex Holomorphic PartMa Lihua0See Keong Lee11Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China)School of Mathematical SciencesIn 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.http://dx.doi.org/10.1155/2022/3450575 |
| spellingShingle | Ma Lihua See Keong Lee Pluriharmonic Mappings with the Convex Holomorphic Part Journal of Mathematics |
| title | Pluriharmonic Mappings with the Convex Holomorphic Part |
| title_full | Pluriharmonic Mappings with the Convex Holomorphic Part |
| title_fullStr | Pluriharmonic Mappings with the Convex Holomorphic Part |
| title_full_unstemmed | Pluriharmonic Mappings with the Convex Holomorphic Part |
| title_short | Pluriharmonic Mappings with the Convex Holomorphic Part |
| title_sort | pluriharmonic mappings with the convex holomorphic part |
| url | http://dx.doi.org/10.1155/2022/3450575 |
| work_keys_str_mv | AT malihua pluriharmonicmappingswiththeconvexholomorphicpart AT seekeonglee pluriharmonicmappingswiththeconvexholomorphicpart |