An optimal irrigation network with infinitely many branching points
Optimization and Control
2014-08-12 v1 Differential Geometry
Functional Analysis
Abstract
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.
Cite
@article{arxiv.1408.2406,
title = {An optimal irrigation network with infinitely many branching points},
author = {Andrea Marchese and Annalisa Massaccesi},
journal= {arXiv preprint arXiv:1408.2406},
year = {2014}
}