Coefficient Groups Inducing Nonbranched Optimal Transport

  • Mircea Petrache

    Pontificia Universidad Católica de Chile, Santiago, Chile
  • Roger Züst

    Universität Bern, Switzerland
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In this work we consider an optimal transport problem with coefficients in a normed Abelian group GG, and extract a purely intrinsic condition on GG that guarantees that the optimal transport (or the corresponding minimum fi lling) is not branching. The condition turns out to be equivalent to the nonbranching of minimum fi llings in geodesic metric spaces. We completely characterize discrete normed groups and finite-dimensional normed vector spaces of coefficients that induce nonbranching optimal transport plans. We also provide a complete classi fication of normed groups for which the optimal transport plans, besides being nonbranching, have acyclic support. This seems to initiate new geometric classifications of certain normed groups. In the nonbranching case we also provide a global version of calibration, i.e. a generalization of Monge–Kantorovich duality.

Cite this article

Mircea Petrache, Roger Züst, Coefficient Groups Inducing Nonbranched Optimal Transport. Z. Anal. Anwend. 37 (2018), no. 4, pp. 389–416

DOI 10.4171/ZAA/1620