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Russian Mathematical Surveys, 2019, Volume 74, Issue 4, Pages 631–657
DOI: https://doi.org/10.1070/RM9899 (Mi rm9899) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Critical configurations of solid bodies and the Morse theory of MIN functions

O. V. Ogievetskyabc, S. B. Shlosmanade

a Aix Marseille Université, Université de Toulon, CNRS, Marseille, France
b P. N. Lebedev Physical Institute of the Russian Academy of Sciences
c Kazan (Volga region) Federal University
d Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
e Skolkovo Institute of Science and Technology
English version PDF (1328 kB) Citations (2)
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DOI: https://doi.org/10.1070/RM9899
Abstract: 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, Platonic configurations, maxima of non-analytic functions.
Funding agency Grant number
Russian Science Foundation 14-50-00150
Labex ANR-11-LABX-0033
University foundation AMIDEX ANR-11-IDEX-0001-02
Ministry of Education and Science of the Russian Federation 5-100
Russian Foundation for Basic Research 17-01-00585
Part of the work of S.B. Shlosman was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences and was supported by the Russian Science Foundation (project no. 14-50-00150). Another part was carried out in the framework of the Labex Archimède programme (grant ANR-11-LABX-0033) and the A*MIDEX project (grant ANR-11-IDEX-0001-02), funded by the ‘Investissements d’Avenir' French Government programme managed by the French National Research Agency (ANR). The work of the O.V. Ogievetsky was supported by the Competitive Growth Programme of Kazan Federal University (project “5-100”) and by the Russian Foundation for Basic Research (grant no. 17-01-00585).
Received: 01.07.2019
Russian version:
Uspekhi Matematicheskikh Nauk, 2019, Volume 74, Issue 4(448), Pages 59–86
DOI: https://doi.org/10.4213/rm9899
Bibliographic databases:
Document Type: Article
UDC: 515.164.1
MSC: 52C17, 52C25
Language: English
Original paper language: Russian
Citation: O. V. Ogievetsky, S. B. Shlosman, “Critical configurations of solid bodies and the Morse theory of MIN functions”, Uspekhi Mat. Nauk, 74:4(448) (2019), 59–86; Russian Math. Surveys, 74:4 (2019), 631–657
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    English version PDF:9
    References:44
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