@article{Baldo2023, 
author = {Sisto Baldo and Van Phu Cuong Le and Annalisa Massaccesi and Giandomenico Orlandi},
title = {Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {4},
pages = {1-19},
keywords = {liquid crystals, optimal mappings, Steiner tree problem, branched optimal transport, homological Plateau problem, G-currents},
url = {https://www.sciopen.com/article/10.3934/mine.2023078},
doi = {10.3934/mine.2023078},
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].}
}