单位圆到凸域的调和映射的Schwarz导数的范数

The Norm of Schwarzian Derivative of Harmonic Mappings which Map the Unit to the Convex Domain

利用单位圆上的保向同胚调和映射的Schwarz导数范数的定义,研究了单位圆到凸域的调和映射的Schwarz导数的范数的性质,得到了单位圆到圆内接正六边形及正八边形的调和映射的Schwarz导数的范数。

In this article makes use of the definition of the Schwarzian derivative of the sense-preserving homeomorphism harmonic mappings in the unit,studies the properties of the norm of Schwarzian derivative of harmonic mappings which map the unit to the convex domain,and obtains the norm of Schwarzian derivative of harmonic mappings which map the unit to the interior of the regular hexagon and octagon inscribed in the unit circle.