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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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\pages 230--236
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    • This publication is cited in the following 7 articles:
    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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