Coefficient groups inducing nonbranched optimal transport

Petrache, Mircea Alexandru; Züst, Roger (2018). Coefficient groups inducing nonbranched optimal transport. Zeitschrift für Analysis und ihre Anwendungen, 37(4), pp. 389-416. EMS Publishing House 10.4171/ZAA/1620

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

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Petrache, Mircea Alexandru and Züst, Roger

Subjects:

500 Science > 510 Mathematics

ISSN:

0232-2064

Publisher:

EMS Publishing House

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

07 May 2019 11:37

Last Modified:

22 Oct 2019 17:30

Publisher DOI:

10.4171/ZAA/1620

BORIS DOI:

10.7892/boris.125486

URI:

https://boris.unibe.ch/id/eprint/125486

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