Geodesic
On the solvability of the discrete analogue of the Minkowski–Alexandrov problem
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 281-288 
V. A. Klyachin. On the solvability of the discrete analogue of the Minkowski–Alexandrov problem. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 281-288. http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The article deals with the multidimensional discrete analogue of the Minkowski problem in the production of A. D. Aleksandrov on the existence of a convex polyhedron with given curvatures at the vertices. We find the conditions for the solvability of this problem in a general setting, when the curvature measure at the polyhedron vertices is defined by an arbitrary continuous function defined on a field $F: \mathbb S^{n-1}\to (0,+\infty)$. The basis for solving the problem is the solvability of the problem whether each triangulation of a finite set of points $ P \subset \mathbb S^{n-1} $ of the unit sphere corresponds a convex polyhedron whose faces normal belong to the set $ P $.

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