Stability and finiteness theorems for Wasserstein spaces

2024/10/04 by Mohammad Alattar
Mathematics · #Geometric Analysis and Curvature Flows #Advanced Mathematical Physics Problems #Advanced Harmonic Analysis Research

paper · doi:10.1090/proc/17084

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.

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• Transport maps, non-branching sets of geodesics and measure rigidity
• On isometries of compact L–Wasserstein spaces

Related

• Stability and Finiteness of Wasserstein Spaces
• Stability and equivariant Gromov--Hausdorff convergence
• Perelman's Stability Theorem
• Gromov-Hausdorff distances for dynamical systems
• Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces