Geodesic
The Plasticity of some Mass Transportation Networks in the Three Dimensional Euclidean Space
Journal of convex analysis, Tome 27 (2020) no. 3, pp. 989-1002
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We obtain an important generalization of the inverse weighted Fermat-Torricelli problem for tetrahedra in R3 by assigning to the corresponding weighted Fermat-Torricelli point a remaining positive number (residual weight). As a consequence, we derive a new plasticity principle of weighted Fermat-Torricelli trees of degree five for boundary closed hexahedra in R3 by applying a geometric plasticity principle which lead to the plasticity of mass transportation networks of degree five in R3. We also derive a complete solution for an important generalization of the inverse weighted Fermat-Torricelli problem for three non-collinear points and a new plasticity principle of mass networks of degree four for boundary convex quadrilaterals in R2. The plasticity of mass transportation networks provides some first evidence for a creation of a new field that we may call Mathematical Botany in the future.
Classification : 51E10, 52A15, 52B10
Mots-clés : Fermat-Torricelli problem, inverse Fermat-Torricelli problem, tetrahedra, plasticity of closed hexahedra, plasticity of quadrilaterals 
@article{JCA_2020_27_3_JCA_2020_27_3_a11,
     author = {A. N. Zachos},
     title = {The {Plasticity} of some {Mass} {Transportation} {Networks} in the {Three} {Dimensional} {Euclidean} {Space}},
     journal = {Journal of convex analysis},
     pages = {989--1002},
     year = {2020},
     volume = {27},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_3_JCA_2020_27_3_a11/}
}
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A. N. Zachos. The Plasticity of some Mass Transportation Networks in the Three Dimensional Euclidean Space. Journal of convex analysis, Tome 27 (2020) no. 3, pp. 989-1002. http://geodesic.mathdoc.fr/item/JCA_2020_27_3_JCA_2020_27_3_a11/