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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 294, Pages 230–236
DOI: https://doi.org/10.1134/S0371968516030134 (Mi tm3742) 		 
This article is cited in 7 scientific papers (total in 7 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
Full-text PDF (164 kB) Citations (7)
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DOI: https://doi.org/10.1134/S0371968516030134
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.
Received: April 18, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 294, Pages 215–221
DOI: https://doi.org/10.1134/S0081543816060134
Bibliographic databases:
Document Type: Article
UDC: 514.12+519.1
Language: Russian
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, Trudy 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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\vol 294
\pages 230--236
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://doi.org/10.1134/S0371968516030134
  • https://www.mathnet.ru/eng/tm/v294/p230
    • This publication is cited in the following 7 articles:
    1. M. I. Shtogrin, “On a convex polyhedron in a regular point system”, Izv. Math., 86:3 (2022), 586–619  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. N. P. Dolbilin, M. I. Shtogrin, “Delone Sets and Tilings: Local Approach”, Proc. Steklov Inst. Math., 318 (2022), 65–89  mathnet  crossref  crossref
    3. M. Bouniaev, N. Dolbilin, “The local theory for regular systems in the context of $t$ -bonded sets”, Symmetry, 10:5 (2018), 159  crossref  mathscinet  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  mathscinet  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  scopus
    6. N. Dolbilin, “Delone sets with congruent clusters”, Struct. Chem., 27:6 (2016), 1725–1732  crossref  isi  scopus
    7. N. P. Dolbilin, “Delone sets in $\mathbb{R}^3$: regularity conditions”, J. Math. Sci., 248:6 (2020), 743–761  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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