Isometric rigidity of Wasserstein tori and spheres

Abstract

We prove isometric rigidity for $p$-Wasserstein spaces over finite-dimensional tori and spheres for all $p$. We present a unified approach to proving rigidity that relies on the robust method of recovering measures from their Wasserstein potentials.

References in corpus (7)

• A geometric study of Wasserstein spaces: Hadamard spaces
• A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces
• A geometric study of Wasserstein spaces: ultrametrics
• Isometric study of Wasserstein spaces --- the real line
• The isometry group of Wasserstein spaces: the Hilbertian case
• On isometric embeddings of Wasserstein spaces -- the discrete case
• Maps on probability measures preserving certain distances --- a survey and some new results

Cited by in corpus (6)

• The isometry group of Wasserstein spaces: the Hilbertian case
• Quantum Wasserstein distance based on an optimization over separable states
• Quantum Wasserstein isometries on the qubit state space
• Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group
• Isometric rigidity of Wasserstein spaces over Euclidean spheres
• Isometric rigidity of the Wasserstein space ${\mathcal{W}}_1(\mathbf{G})$ over Carnot groups