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| The Schwarzian Derivative of Harmonic Mappings in the Plane |
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Citation： |
Liping NIE,Zongxin YANG.The Schwarzian Derivative of Harmonic Mappings in the Plane[J].Chinese Annals of Mathematics B,2020,41(2):193~208 |
| Page view： 955
Net amount： 792 |
Authors： |
Liping NIE; Zongxin YANG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11261022). |
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| Abstract： |
In this paper, the authors introduce a definition of the Schwarzian
derivative of any locally univalent harmonic mapping defined on a
simply connected domain in the complex plane. Using the new
definition, the authors prove that any harmonic mapping $f$ which
maps the unit disk onto a convex domain has Schwarzian norm
$\|S_{f}\|\leq6$. Furthermore, any locally univalent harmonic
mapping $f$ which maps the unit disk onto an arbitrary regular
$n$-gon has Schwarzian norm $\|S_{f}\|\leq\frac{8}{3}$. |
Keywords： |
Schwarzian derivative, Schwarzian norm, Harmonic mapping |
Classification： |
30C55, 30C62 |
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