Decomposition of acyclic normal currents in a metric space

Abstract

We prove that every acyclic normal one-dimensional real Ambrosio-Kirchheim current in a Polish (i.e. complete separable metric) space can be decomposed in curves, thus generalizing the analogous classical result proven by S. Smirnov in Euclidean space setting. The same assertion is true for every complete metric space under a suitable set-theoretic assumption.

Cited by in corpus (12)

• Structure of measures in Lipschitz differentiability spaces
• The Steiner tree problem revisited through rectifiable G-currents
• A multi-material transport problem with arbitrary marginals
• Semicontinuity of eigenvalues under intrinsic flat convergence
• Improved stability of optimal traffic paths
• On the structure of divergence-free measures on ${\mathbb{R}}^2$
• On the well-posedness of branched transportation
• A Henstock-Kurzweil type integral on 1 dimensional integral currents
• Examples of $2$-unrectifiable normal currents
• Metric currents and the Poincaré inequality
• Cyclically monotone non-optimal $N$-marginal transport plans and Smirnov-type decompositions for $N$-flows
• Ramified optimal transportation with payoff on the boundary