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| On the Univalence and Quasiconformal Extensions Criterion for Harmonic Mappings Associated with Pre-Schwarzian Derivative |
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Citation： |
Xiaoyuan WANG,Jinhua FAN,Zhenyong HU,Zhigang WANG.On the Univalence and Quasiconformal Extensions Criterion for Harmonic Mappings Associated with Pre-Schwarzian Derivative[J].Chinese Annals of Mathematics B,2026,(3):475~490 |
| Page view： 96
Net amount： 47 |
Authors： |
Xiaoyuan WANG; Jinhua FAN;Zhenyong HU;Zhigang WANG |
Foundation： |
National Natural Science Foundation of China (No.12471074), the China Scholarship Council (No.202306840137), the Natural Science Foundation of Henan Province (No.252300420942), the Postgraduate Research and Practice Innovation Program of Jiangsu Province (No.KYCX230410), the Key Project of Education Department of Hunan Province (No.25A0668) and the Natural Science Foundation of Changsha (No. kq2502003). |
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| Abstract： |
As a generalization of Ahlfors's results for analytic functions, by using the pre-Schwarzian derivative of harmonic mappings, the authors obtain a criterion of univalence and quasiconformal extension for harmonic functions. As applications, they give a lower bound of the inner radius of univalency by means of pre-Schwarzian derivative of harmonic mappings for a planar domain. |
Keywords： |
Harmonic mapping Quasiconformal extension Pre-Schwarzian derivative Inner radius of univalency |
Classification： |
30C55, 31C45, 30C62, 31A05 |
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