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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
An optimal irrigation network with infinitely many branching points
Andrea Marchese and Annalisa MassaccesiAbstract
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.
- Received:
- 04.08.14
- Published:
- 07.08.14
- MSC Codes:
- 49Q15, 49Q20, 49N60, 53C38
- Keywords:
- Gilbert-Steiner problem, irrigation problem, calibrations, flat G-chains