Calculus of Variations and Geometric Measure Theory
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L. Granieri

Remarks on the stability of mass minimizing currents in the Monge-Kantorovich problem

created by granieri on 21 Apr 2010
modified on 08 Mar 2012


Published Paper

Inserted: 21 apr 2010
Last Updated: 8 mar 2012

Journal: Indagationes Mathematicae
Volume: 20
Number: 4
Pages: 527-536
Year: 2009


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.

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