For citation:
Klyachin V. A. On the Solvability of the Discrete Analogue of the Minkowski – Alexandrov Problem. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 3, pp. 281-288. DOI: 10.18500/1816-9791-2016-16-3-281-288, EDN: WMIIGN
On the Solvability of the Discrete Analogue of the Minkowski – Alexandrov Problem
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 : S n−1 → (0, +∞). The basis for solving the problem is the solvability of the problem whether each triangulation of a finite set of points P ⊂ S n−1 of the unit sphere corresponds a convex polyhedron whose faces normal belong to the set P.
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