Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks

We investigate the relation between energy minimizing maps valued into spheres having topological singularities at given points and optimal networks connecting them (e.g. Steiner trees, Gilbert-Steiner irrigation networks). We show the equivalence of the corresponding variational problems, interpret...

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Bibliographic Details
Published in:arXiv.org 2023-02
Main Authors: Sisto Baldo, Van Phu Cuong Le, Massaccesi, Annalisa, Orlandi, Giandomenico
Format: Article
Language:English
Subjects:
Homology
Networks
Singularities
Online Access:Get full text
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Summary:We investigate the relation between energy minimizing maps valued into spheres having topological singularities at given points and optimal networks connecting them (e.g. Steiner trees, Gilbert-Steiner irrigation networks). We show the equivalence of the corresponding variational problems, interpreting in particular the branched optimal transport problem as a homological Plateau problem for rectifiable currents with values in a suitable normed group. This generalizes the pioneering work by Brezis, Coron and Lieb [10].
ISSN:2331-8422