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

2021/12/23 by Sisto Baldo, Baldo, Sisto, Van Phu Cuong Le +5 · 1 citation
Computer Science · Engineering · #49Q10 #49Q15 #49Q20 #53C38 #58E20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Slime Mold and Myxomycetes Research #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2112.12511

openalex publication_date 2021/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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