On the Optimality of Functionals over Triangulations of Delaunay Sets
  In this short paper, we consider the functional density on sets of uniformly bounded triangulations with fixed sets of vertices. We prove that if a functional attains its minimum on the Delaunay triangulation, for every finite set in the plane, then for infinite sets the density of this functional attains its minimum also on the Delaunay triangulations. 
Nikolay P. Dolbilin, Herbert Edelsbrunner and Oleg R. Musin
math.MG