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arXiv · 2112.12511

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

Sisto Baldo·Van Phu Cuong Le·Annalisa Massaccesi·Giandomenico Orlandi
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Abstract

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].

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Sisto Baldo, Van Phu Cuong Le, Annalisa Massaccesi, Giandomenico Orlandi. 2021-12-23. Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks. https://arxiv.org/abs/2112.12511

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