Geodesic
Description of functionals that are minimized by $\Phi$-triangulations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 139 (2017), pp. 9-14.

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We obtain condition for a function $f$ defined on the set of simplexes $S$ under which the values $F(T)=\sum\limits_{S\in T}f(S)$ or $F_f^m(T)=\max\limits_{S\in T}f(S)$ are minimal for $\Phi$-triangulations of $T$. As consequences, we also obtain certain extremal properties of the classical Delaunay triangulation.
Mots-clés : triangulation, Delaunay condition
Keywords: empty sphere, functional. 
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     author = {V. A. Klyachin and E. G. Grigorieva},
     title = {Description of functionals that are minimized by $\Phi$-triangulations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {9--14},
     publisher = {mathdoc},
     volume = {139},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_139_a1/}
}
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V. A. Klyachin; E. G. Grigorieva. Description of functionals that are minimized by $\Phi$-triangulations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 139 (2017), pp. 9-14. http://geodesic.mathdoc.fr/item/INTO_2017_139_a1/