论文标题
具有圆锥边界的域上蓝雪样地图的几何特性
Geometric properties of Blaschke-like maps on domains with a conic boundary
论文作者
论文摘要
对于单位磁盘中包含的圆圈$ C $，对于单位圆圈中刻有三角形的必要条件和大约$ c $的三角形被称为Chapple的公式。 Daepp等人给出的Blaschke第3级产品的几何特性。 （2002）和Frantz（2004）允许我们将Chapple的公式扩展到单元磁盘中的椭圆情况。本文的主要目的是提供Chapple公式的进一步扩展。在边界是圆锥的域中引入了一个类似Blaschke的图，我们将其结果扩展到外部曲线是椭圆或抛物线的情况。此外，我们还为$ d $的Blaschke样地图提供了一些几何属性。
For a circle $ C $ contained in the unit disk, the necessary and sufficient condition for the existence of a triangle inscribed in the unit circle and circumscribed about $ C $ is known as Chapple's formula. The geometric properties of Blaschke products of degree 3 given by Daepp et al. (2002) and Frantz (2004) allow us to extend Chapple's formula to the case of ellipses in the unit disk. The main aim of this paper is to provide a further extension of Chapple's formula. Introducing a Blaschke-like map of a domain whose boundary is a conic, we extend their results to the case where the outer curve is an ellipse or a parabola. Moreover, we also give some geometrical properties for the Blaschke-like maps of degree $ d $.
