Harmonic mappings valued in the Wasserstein space
Hugo Lavenant, Institut de Mathématique d'Orsay Univ. Paris-Sud
Aula Beltrami, Dipartimento di Matematica - Wednesday, March 13, 2019 h.15:00
Abstract. The Wasserstein space, which is the space of probability measures endowed with the so-called (quadratic) Wasserstein distance coming from optimal transport, can formally be seen as a Riemannian manifold of infinite dimension. We propose, through a variational approach, a definition of harmonic mappings defined over a domain of an Euclidean space and valued in the Wasserstein space. We will show how one can build a fairly satisfying theory which captures some key features of harmonicity and present a numerical scheme to compute such harmonic mappings. Other than a better understanding of the Wasserstein space, the motivation of such a study can be found in geometric data analysis.
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