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Stability and Finiteness of Wasserstein Spaces (2406.05998v1)
Published 10 Jun 2024 in math.MG and math.DG
Abstract: Under Gromov--Hausdorff convergence, and equivariant Gromov--Hausdorff convergence, we prove stability results of Wasserstein spaces over certain classes of singular and non-singular spaces. For example, we obtain an analogue of Perelman's stability theorem on Wasserstein spaces.
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