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This article is cited in 2 scientific papers (total in 2 papers)
Functionals on triangulations of Delaunay sets
Nikolay P. Dolbilina, Herbert Edelsbrunnerb, Alexey Glazyrinc, Oleg R. Musincd a Department of Geometry and Topology, Steklov Mathematical Institute, 8, Gubkina str., 119991, Moscow, Russia
b Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria
c Department of Mathematics, University of Texas at Brownsville, One West University Boulevard, Brownsville, Texas 78520, USA
d The Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow, 127994, Russia
Abstract:
We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.
Key words and phrases:
Delaunay sets, triangulations, Delaunay triangulations, uniformly bounded triangulations, functionals, densities.
DOI:
https://doi.org/10.17323/1609-4514-2014-14-3-491-504
Full text:
http://www.mathjournals.org/.../2014-014-003-003.html
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Bibliographic databases:
MSC: 52C20, 52C22 Received: January 13, 2012
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Citation:
Nikolay P. Dolbilin, Herbert Edelsbrunner, Alexey Glazyrin, Oleg R. Musin, “Functionals on triangulations of Delaunay sets”, Mosc. Math. J., 14:3 (2014), 491–504
Citation in format AMSBIB
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\by Nikolay~P.~Dolbilin, Herbert~Edelsbrunner, Alexey~Glazyrin, Oleg~R.~Musin
\paper Functionals on triangulations of Delaunay sets
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 3
\pages 491--504
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http://mi.mathnet.ru/eng/mmj530 http://mi.mathnet.ru/eng/mmj/v14/i3/p491
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This publication is cited in the following articles:
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V. A. Klyachin, “Ekstremalnye svoistva triangulyatsii, osnovannoi na uslovii pustogo vypuklogo mnozhestva”, Sib. elektron. matem. izv., 12 (2015), 991–997
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H. Edelsbrunner, A. Glazyrin, O. R. Musin, A. Nikitenko, “The Voronoi functional is maximized by the Delaunay triangulation in the plane”, Combinatorica, 37:5 (2017), 887–910
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