多边形的极值区域，沿圆滑动

IF 0.6 4区数学 Q3 MATHEMATICS

Hokkaido Mathematical Journal Pub Date : 2020-01-29 DOI:10.14492/hokmj/2020-312

D. Siersma

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引用次数: 3

摘要

我们确定了顶点在圆形或椭圆上的多边形上的Area函数的所有关键配置。对于孤立的临界点，我们计算了它们的莫尔斯指数，梯度矢量场的resp指数。我们将孤立退化点处的计算与关于组合的特征值问题联系起来。在偶维情况下，非孤立奇点以“之字形列车”的形式出现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Extremal Area of Polygons, sliding along a circle

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'.

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来源期刊

Hokkaido Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The main purpose of Hokkaido Mathematical Journal is to promote research activities in pure and applied mathematics by publishing original research papers. Selection for publication is on the basis of reports from specialist referees commissioned by the editors.