Rendiconti del Seminario Matematico della Università di Padova

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Volume 124, 2010, pp. 91–125
DOI: 10.4171/RSMUP/124-6

Published online: 2010-12-31

Metric Currents and Geometry of Wasserstein Spaces

Luca Granieri[1]

(1) 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 Tn, we prove that the space Pp(Tn) 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 Tn corresponds to a mass minimizing metric current on Pp(Tn) in its homology class.

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Granieri Luca: Metric Currents and Geometry of Wasserstein Spaces. Rend. Sem. Mat. Univ. Padova 124 (2010), 91-125. doi: 10.4171/RSMUP/124-6