Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik Moskov. Univ. Ser. 1. Mat. Mekh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, Number 5, Pages 3–8 (Mi vmumm522)  

This article is cited in 6 scientific papers (total in 6 papers)

Mathematics

One-dimensional minimal fillings with negative edge weights

A. O. Ivanov, Z. N. Ovsyannikov, N. P. Strelkova, A. A. Tuzhilin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A. O. Ivanov and A. A. Tuzhilin started an investigation of a particular case of Gromov Minimal Fillings problem generalization to the case of stratified manifolds using weighted graphs with nonnegative weight function as minimal fillings of finite metric spaces. In this paper we introduce generalized minimal fillings, i.e., minimal fillings where the weight function is not necessarily nonnegative. We prove that for any finite metric space its minimal filling has the minimum weight in the class of its generalized fillings.

Key words: minimal filling, finite metric spaces.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00748
Ministry of Education and Science of the Russian Federation НШ-1410.2012.1
11.G34.31.0053


Full text: PDF file (280 kB)
References: PDF file   HTML file

English version:
Moscow University Mathematics Bulletin, 2012, 67:5-6, 189–194

Bibliographic databases:

UDC: 514.774.8+515.124.4+519.176
Received: 13.12.2010

Citation: A. O. Ivanov, Z. N. Ovsyannikov, N. P. Strelkova, A. A. Tuzhilin, “One-dimensional minimal fillings with negative edge weights”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 5, 3–8; Moscow University Mathematics Bulletin, 67:5-6 (2012), 189–194

Citation in format AMSBIB
\Bibitem{IvaOvsStr12}
\by A.~O.~Ivanov, Z.~N.~Ovsyannikov, N.~P.~Strelkova, A.~A.~Tuzhilin
\paper One-dimensional minimal fillings with negative edge weights
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 5
\pages 3--8
\mathnet{http://mi.mathnet.ru/vmumm522}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076491}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2012
\vol 67
\issue 5-6
\pages 189--194
\crossref{https://doi.org/10.3103/S0027132212050014}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870934705}


Linking options:
  • http://mi.mathnet.ru/eng/vmumm522
  • http://mi.mathnet.ru/eng/vmumm/y2012/i5/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. Yu. Eremin, “A formula for the weight of a minimal filling of a finite metric space”, Sb. Math., 204:9 (2013), 1285–1306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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
    3. 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, eds. A. Barg, O. Musin, Amer. Math. Soc., 2014, 9–35  crossref  mathscinet  zmath  isi
    4. 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
    5. A. O. Ivanov, A. A. Tuzhilin, “Analiticheskie deformatsii minimalnykh setei”, Fundament. i prikl. matem., 21:5 (2016), 159–180  mathnet
    6. A. O. Ivanov, A. A. Tuzhilin, “Minimal networks: a review”, Advances in Dynamical Systems and Control, Studies in Systems Decision and Control, 69, eds. V. Sadovnichiy, M. Zgurovsky, Springler, 2016, 43–80  crossref  mathscinet  zmath  isi  scopus
  • Number of views:
    This page:70
    Full text:17
    References:10

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021