Stability and Finiteness of Wasserstein Spaces
Mohammad Alattar
TL;DR
This paper proves stability results for Wasserstein spaces under Gromov--Hausdorff convergence, including an analogue of Perelman's stability theorem, applicable to both singular and non-singular spaces.
Contribution
It establishes stability theorems for Wasserstein spaces in the context of Gromov--Hausdorff convergence, extending Perelman's stability to Wasserstein spaces.
Findings
Stability of Wasserstein spaces under Gromov--Hausdorff convergence
Analogue of Perelman's stability theorem for Wasserstein spaces
Applicability to singular and non-singular spaces
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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Taxonomy
TopicsIntracerebral and Subarachnoid Hemorrhage Research · Soft tissue tumor case studies · Geometric and Algebraic Topology