Preprint
Aug 2026
Metric Geometry of Lebesgue, Wasserstein, and Gromov-Wasserstein Spaces: Submetries, Curvature, and Geodesics
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 Lebesgue $L^p$-spaces of $Z$-valued maps, and $p$-Gromov-Wasserstein spaces of $Z$-valued kernels. The latter class, referred to as $Z$-Gromov-...
Martin Bauer, Facundo Mémoli, Tom Needham et al.
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