Description of Functionals that are Minimized by Φ-Triangulations

Abstract

We obtain condition for a function f defined on the set of simplexes S under which the values \( F(T)=\sum \limits_{S\in T}f(S)\;\mathrm{or}\;{F}_f^m(T){=}_{S\in T}^{\mathrm{max}}f(S) \) are minimal for Φ-triangulations of T . As consequences, we also obtain certain extremal properties of the classical Delone triangulation.