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Tr. Mat. Inst. Steklova, 2016, Volume 294, Pages 230–236 (Mi tm3742)  

This article is cited in 5 scientific papers (total in 5 papers)

Uniqueness theorem for locally antipodal Delaunay sets

N. P. Dolbilin, A. N. Magazinov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We prove theorems on locally antipodal Delaunay sets. The main result is the proof of a uniqueness theorem for locally antipodal Delaunay sets with a given $2R$-cluster. This theorem implies, in particular, a new proof of a theorem stating that a locally antipodal Delaunay set all of whose $2R$-clusters are equivalent is a regular system, i.e., a Delaunay set on which a crystallographic group acts transitively.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968516030134

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 215–221

Bibliographic databases:

UDC: 514.12+519.1
Received: April 18, 2016

Citation: N. P. Dolbilin, A. N. Magazinov, “Uniqueness theorem for locally antipodal Delaunay sets”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 230–236; Proc. Steklov Inst. Math., 294 (2016), 215–221

Citation in format AMSBIB
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\inbook Modern problems of mathematics, mechanics, and mathematical physics.~II
\bookinfo Collected papers
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\pages 230--236
\publ MAIK Nauka/Interperiodica
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Dolbilin, “Delone sets with congruent clusters”, Struct. Chem., 27:6 (2016), 1725–1732  crossref  isi  scopus
    2. N. P. Dolbilin, “Mnozhestva Delone v $\mathbb{R}^3$: uslovie pravilnosti”, Fundament. i prikl. matem., 21:6 (2016), 115–141  mathnet
    3. M. Bouniaev, N. Dolbilin, “The local theory for regular systems in the context of $t$ -bonded sets”, Symmetry, 10:5 (2018), 159  crossref  isi  scopus
    4. N. P. Dolbilin, “Delone sets in $\mathbb R^3$ with $2R$-regularity conditions”, Proc. Steklov Inst. Math., 302 (2018), 161–185  mathnet  crossref  crossref  isi  elib
    5. I. A. Baburin, M. Bouniaev, N. Dolbilin, N. Yu. Erokhovets, A. Garber, S. V. Krivovichev, E. Schulte, “On the origin of crystallinity: a lower bound for the regularity radius of Delone sets”, Acta Crystallogr. Sect. A, 74:6 (2018), 616–629  crossref  mathscinet  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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