Moscow Mathematical Journal

Volume 14, Issue 3, July–September 2014 pp. 491–504.

Functionals on Triangulations of Delaunay Sets

Authors: N. Dolbilin (1), H. Edelsbrunner (2), A. Glazyrin (3), and O. Musin (4)
Author institution:(1) Department of Geometry and Topology, Steklov Mathematical Institute, 8, Gubkina str., 119991, Moscow, Russia
(2) Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria
(3) Department of Mathematics, University of Texas at Brownsville, One West University Boulevard, Brownsville, Texas 78520, USA
(4) Department of Mathematics, University of Texas at Brownsville, One West University Boulevard, Brownsville, Texas 78520, USA and The Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow, 127994, Russia

Summary:

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.

2010 Mathematics Subject Classification. 52C20, 52C22.

Keywords: Delaunay sets, triangulations, Delaunay triangulations, uniformly bounded triangulations, functionals, densities.

Contents Full-Text PDF