论文标题
多边形的极端区域，沿圆圈滑动
Extremal Area of Polygons, sliding along a Circle
论文作者
论文摘要
我们确定在多边形上具有圆或椭圆形的顶点的区域功能的所有关键配置。对于孤立的临界点，我们计算其MORSE指数，梯度向量场的RESP指数。我们将计算在孤立的退化点与有关组合的特征值问题联系起来。在均匀的情况下，非分离的奇异性发生在“曲折火车”中。
We determine all critical configurations for the Area function on polygons with vertices on a circle or an ellipse. For isolated critical points we compute their Morse index, resp index of the gradient vector field. We relate the computation at an isolated degenerate point to an eigenvalue question about combinations. In the even dimensional case non-isolated singularities occur as `zigzag trains'.
