Inserted: 21 apr 2010
Last Updated: 8 mar 2012
Journal: Indagationes Mathematicae
The Monge-Kantorovich problem is equivalent to the problem of finding $1$-currents with fixed boundary and minimal mass. We address the question of the stability for the mass minimizing currents. In particular, we state a $\Gamma$-convergence result. We provide proofs relying just on basic properties of currents and on the notion of flat norm.