We describe a convex relaxation for the Gilbert-Steiner problem both in Rd and on manifolds, extending the framework proposed in [9], and we discuss its sharpness by means of calibration type arguments. The minimization of the resulting problem is then tackled numerically and we present results for an extensive set of examples. In particular we are able to address the Steiner tree problem on surfaces.
@article{arxiv.1810.05417,
title = {A convex approach to the Gilbert-Steiner problem},
author = {Mauro Bonafini and Édouard Oudet},
journal= {arXiv preprint arXiv:1810.05417},
year = {2018}
}