Rendiconti del Seminario Matematico della Università di Padova
Full-Text PDF (327 KB) | Metadata | Table of Contents | RSMUP summary
Published online: 2010-12-31
Metric Currents and Geometry of Wasserstein SpacesLuca Granieri (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.
No keywords available for this article.
Granieri Luca: Metric Currents and Geometry of Wasserstein Spaces. Rend. Sem. Mat. Univ. Padova 124 (2010), 91-125. doi: 10.4171/RSMUP/124-6