Geodesic
Critical configurations of solid bodies and the Morse theory of MIN functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 4, pp. 631-657

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This paper studies the manifold of clusters of non-intersecting 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. The notion of critical cluster is introduced, and several critical clusters of balls and of cylinders are studied. In the case of cylinders, some of the critical clusters here are new. The paper also establishes criticality properties of clusters introduced earlier by Kuperberg [7].
Keywords: configurations of balls, configurations of cylinders, rigid clusters, flexible clusters, critical clusters, connected components, Galois symmetries, maxima of non-analytic functions.
Mots-clés : Platonic configurations 
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     title = {Critical configurations of solid bodies and the {Morse} theory of {MIN} functions},
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O. V. Ogievetsky; S. B. Shlosman. Critical configurations of solid bodies and the Morse theory of MIN functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 4, pp. 631-657. http://geodesic.mathdoc.fr/item/RM_2019_74_4_a1/