Metric Currents and Geometry of Wasserstein Spaces

  • Luca Granieri

    Università degli Studi di Bari, Italy


We investigate some geometric aspects of Wasserstein spaces through the continuity equation as worked out in mass transportation theory. By defining a suitable homology on the flat torus , we prove that the space has non-trivial homology in a metric sense. As a byproduct of the developed tools, we show that every parametrization of a Mather’s minimal measure on corresponds to a mass minimizing metric current on in its homology class.

Cite this article

Luca Granieri, Metric Currents and Geometry of Wasserstein Spaces. Rend. Sem. Mat. Univ. Padova 124 (2010), pp. 91–125

DOI 10.4171/RSMUP/124-6