论文标题
多边形的极端区域沿曲线滑动
Extremal Area of Polygons sliding along Curves
论文作者
论文摘要
在本文中，我们研究多边形的面积功能，顶点沿曲线滑动。我们给出临界点的几何标准，并在这些点上确定黑森矩阵。这是摩尔斯理论方法的起点，其中包括与配置空间拓扑的关系。此外，极端区域的状况引起了一种新型的台球类型：内部区域台球。
In this paper we study the area function of polygons, where the vertices are sliding along curves. We give geometric criteria for the critical points and determine also the Hesse matrix at those points. This is the starting point for a Morse-theoretic approach, which includes the relation with the topology of the configuration spaces. Moreover the condition for extremal area gives rise to a new type of billiard: the inner area billiard.
