The Schwarzian Derivative of Harmonic Mappings in the Plane 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： 200        Net amount： 203 Authors： Liping NIE; Zongxin YANG Foundation： This work was supported by the National Natural Science Foundation of China (No.11261022). 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 Download PDF Full-Text