Metric Geometry of Lebesgue, Wasserstein, and Gromov-Wasserstein Spaces: Submetries, Curvature, and Geodesics

Martin Bauer, Facundo Mémoli, Tom Needham +1

A metric space $Z$ gives rise to three natural classes of infinite-dimensional metric spaces associated to $Z$: $p$-Wasserstein spaces of probability measures on $Z$, nonlinear Leb…