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The plasticity of some mass transportation networks in the three dimensional Euclidean space. (English) Zbl 1448.51004

The author formulates some inverse mixed weighted Fermat-Torricelli problems (essentially asking, given a figure and a point \(P\) inside it, to find weights satisfying various conditions, so that a certain weighted sum achieves its minimum at \(P\)) and solves them for the tetrahedron and the triangle.

MSC:

51E10 Steiner systems in finite geometry
52A15 Convex sets in \(3\) dimensions (including convex surfaces)
52B10 Three-dimensional polytopes
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References:

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