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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, Number 2, Pages 8–11 (Mi vmumm471)  

This article is cited in 4 scientific papers (total in 4 papers)

Mathematics

The additivity criterion for finite metric spaces and minimal fillings

O. V. Rubleva

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A new additivity criterion of a finite metric space is obtained in the paper. The criterion is based on properties of minimal trees in Gromov's case.

Key words: metric spaces, additivity spaces, minimal fillings in Gromov's case, Steiner minimal trees.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00748
Ministry of Education and Science of the Russian Federation НШ-3224.2010.1
02.740.11.5213
11.G34.31.0053


Full text: PDF file (209 kB)
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English version:
Moscow University Mathematics Bulletin, 2012, 67:2, 52–54

Bibliographic databases:

UDC: 514.774.8+515.124.4+519.17
Received: 16.09.2010

Citation: O. V. Rubleva, “The additivity criterion for finite metric spaces and minimal fillings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 2, 8–11; Moscow University Mathematics Bulletin, 67:2 (2012), 52–54

Citation in format AMSBIB
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\by O.~V.~Rubleva
\paper The additivity criterion for finite metric spaces and minimal fillings
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 2
\pages 8--11
\mathnet{http://mi.mathnet.ru/vmumm471}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2985887}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2012
\vol 67
\issue 2
\pages 52--54
\crossref{https://doi.org/10.3103/S0027132212020027}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870337928}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. O. Ivanov, A. A. Tuzhilin, “Gromov minimal fillings for finite metric spaces”, Publ. Inst. Math.-Beograd, 94:108 (2013), 3–15  crossref  mathscinet  zmath  isi  scopus
    2. A. O. Ivanov, A. A. Tuzhilin, “Minimal fillings of finite metric spaces: the state of the art”, Discrete Geometry and Algebraic Combinatorics, Contemporary Mathematics, 625, ed. A. Barg, O. Musin, Amer. Math. Soc., 2014, 9–35  crossref  mathscinet  zmath  isi
    3. S. Yu. Lipatov, “The functions that do not change types of minimal fillings”, Moscow University Mathematics Bulletin, 70:6 (2015), 267–269  mathnet  crossref  mathscinet  isi
    4. A. O. Ivanov, A. A. Tuzhilin, “Minimal networks: a review”, Advances in Dynamical Systems and Control, Studies in Systems Decision and Control, 69, ed. V. Sadovnichiy, M. Zgurovsky, Springler, 2016, 43–80  crossref  mathscinet  zmath  isi  scopus
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