固体的临界位形与MIN函数的莫尔斯理论
Critical configurations of solid bodies and the Morse theory of MIN functions
摘要：
我们研究了不相交全等固体团簇的流形，这些团簇都与半径为1的中心球$B\subset\mathbb{R}^{3}$接触。两个主要的例子是球簇和无限长圆柱簇。我们介绍了\textit{critical cluster}的概念，我们研究了几个关键集团的球和圆柱。对于圆柱体的情况，我们的一些关键集群是新的。我们还建立了团簇的临界性质，介绍了W。库珀伯格
英文摘要：
We study the manifold of clusters of nonintersecting congruent solid bodies, all touching the central ball $B\subset\mathbb{R}^{3}$ of radius one. Two main examples are clusters of balls and clusters of infinite cylinders. We introduce the notion of \textit{critical cluster} and we study several critical clusters of balls and of cylinders. For the case of cylinders some of our critical clusters are new. We also establish the criticality properties of clusters, introduced earlier by W. Kuperberg.
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