以无穷远点为内点的区域的单叶性内径(英文)

On the Inner Radius of Univalency of Plane Domains Containing the Point ∞

研究了以无穷远点为内点的平面区域的Schwarz导数及pre-Schwarz导数单叶性内径问题,给出了一个pre-Schwarz导数单叶性内径下界公式的推广,还得到了一类正规圆弧三角形外部区域的Schwarz导数单叶性内径的精确值.

The inner radius of univalency of plane domains which have ∞ as interior point by the Schwarzian derivative and the pre-Schwarzian derivative are studied. A formula for the lower bound of the inner radius by pre- Schwarzian derivative is generalized, and the inner radius for the exterior domains of a class of normal circular triangles by the Schwarzian derivative is also obtained.