The plasticity of some mass transportation networks in the three dimensional Euclidean Space

2017/04/24 by Zachos, Anastasios
#51E10 #52A15 #52B10 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1704.07473

Abstract

We obtain an important generalization of the inverse weighted Fermat-Torricelli problem for tetrahedra in R³ by assigning at the corresponding weighted Fermat-Torricelli point a remaining positive number (residual weight). As a consequence, we derive a new plasticity principle of weighted Fermat-Torricellitrees 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 in a creation of a new field that we may call in the future Mathematical Botany.

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