Critical configurations of solid bodies and the Morse theory of MIN functions
- 作者: Ogievetskii O.V.1,2,3, Shlosman S.B.1,4,5
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隶属关系:
- Aix-Marseille Université
- P. N. Lebedev Physical Institute of the Russian Academy of Sciences
- Kazan (Volga Region) Federal University
- Institute for Information Transmission Problems, Russian Academy of Sciences
- Skolkovo Institute of Science and Technology
- 期: 卷 74, 编号 4 (2019)
- 页面: 59-86
- 栏目: Articles
- URL: https://ogarev-online.ru/0042-1316/article/view/133563
- DOI: https://doi.org/10.4213/rm9899
- ID: 133563
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详细
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].
作者简介
Oleg Ogievetskii
Aix-Marseille Université; P. N. Lebedev Physical Institute of the Russian Academy of Sciences; Kazan (Volga Region) Federal University
Email: oleg@cpt.univ-mrs.fr
Candidate of physico-mathematical sciences
Semen Shlosman
Aix-Marseille Université; Institute for Information Transmission Problems, Russian Academy of Sciences; Skolkovo Institute of Science and Technology
Email: shlosman@cpt.univ-mrs.fr
Doctor of physico-mathematical sciences
参考
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- W. Kuperberg, “How many unit cylinders can touch a unit ball? (Problem 3.3)”, DIMACS Workshop on polytopes and convex sets, Rutgers Univ., 1990
- R. Kusner, W. Kusner, J. C. Lagarias, S. Shlosman, “Configuration spaces of equal spheres touching a given sphere: the twelve spheres problem”, New trends in intuitive geometry, Bolyai Soc. Math. Stud., 27, Janos Bolyai Math. Soc., Budapest, 2018, 219–277
- J. C. Lagarias (ed.), The Kepler conjecture. The Hales–Ferguson proof, Springer, New York, 2011, xiv+456 pp.
- O. Ogievetsky, S. Shlosman, “The six cylinders problem: $mathbb D_{3}$-symmetry approach”, Discrete Comput. Geom., publ. online 2019, 1–20
- O. Ogievetsky, S. Shlosman, Extremal cylinder configurations I: Configuration $C_{mathfrak{m}}$, 2018, 38 pp.
- O. Ogievetsky, S. Shlosman, Extremal cylinder configurations II: Configuration $O_{6}$, 2019, 25 pp.
- O. Ogievetsky, S. Shlosman, Platonic compounds of cylinders, 2019, 35 pp.
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