2014/08/11 by Andrea Marchese, Marchese, Andrea, Annalisa Massaccesi +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #49N60 #49Q15 #49Q20 #53C38 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #Diffusion and Search Dynamics #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.1408.2406
openalex publication_date 2014/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Gilbert-Steiner problem is a mass transportation problem, where the cost of the transportation depends on the network used to move the mass and it is proportional to a certain power of the "flow". In this paper, we introduce a new formulation of the problem, which turns it into the minimization of a convex functional in a class of currents with coefficients in a group. This framework allows us to define calibrations, which can be used to prove the optimality of concrete configurations. We apply this technique to prove the optimality of a certain irrigation network, having the topological property mentioned in the title.