Nikolay P. Dolbilin, Herbert Edelsbrunner, Alexey Glazyrin, Oleg R. Musin, “Functionals on triangulations of Delaunay sets”, Mosc. Math. J., 2014, Volume 14, Number 3,Pages <nobr>491–504</nobr>

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Mosc. Math. J., 2014 Volume 14, Number 3, Pages 491–504 (Mi mmj530)

This article is cited in 3 papers

Functionals on triangulations of Delaunay sets

Nikolay P. Dolbilin^a, Herbert Edelsbrunner^b, Alexey Glazyrin^c, Oleg R. Musin^cd

^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.

MSC: 52C20, 52C22

Received: January 13, 2012

Language: English

DOI: 10.17323/1609-4514-2014-14-3-491-504

Fulltext: www.mathjournals.org/.../2014-014-003-003.html
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