A GEOMETRIC STUDY OF WASSERSTEIN SPACES: HADAMARD SPACES

DOI10.1142/S1793525312500227zbMath1263.53026arXiv1010.0590OpenAlexW3105956282WikidataQ125890028 ScholiaQ125890028MaRDI QIDQ4908235

Jérôme Bertrand, Benoît R. Kloeckner

Publication date: 5 March 2013

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.0590

zbMATH Keywords

CAT(0) spacenon-positive curvatureflatsoptimal transportvisual boundaryWasserstein space

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Global Riemannian geometry, including pinching (53C20) Spaces of measures, convergence of measures (28A33)

Related Items (13)

Geometric Averages of Partitioned Datasets ⋮ Busemann functions on the Wasserstein space ⋮ Convergence analysis of the extragradient method for equilibrium problems in Hadamard spaces ⋮ Isometric rigidity of Wasserstein tori and spheres ⋮ Universal regular conditional distributions via probabilistic transformers ⋮ Quantum Wasserstein isometries on the qubit state space ⋮ Horo-functions associated to atom sequences on the Wasserstein space ⋮ Isometric study of Wasserstein spaces – the real line ⋮ A GEOMETRIC STUDY OF WASSERSTEIN SPACES: ULTRAMETRICS ⋮ Network Consensus in the Wasserstein Metric Space of Probability Measures ⋮ Nonpositive curvature, the variance functional, and the Wasserstein barycenter ⋮ On isometric embeddings of Wasserstein spaces -- the discrete case ⋮ On isometries of compact \(L^p\)-Wasserstein spaces

Cites Work

• Unnamed Item
• Some geometric calculations on Wasserstein space
• Hyperbolic buildings, conformal dimension and Mostow rigidity
• A convexity principle for interacting gases
• Ricci curvature for metric-measure spaces via optimal transport
• On the geometry of metric measure spaces. II
• Visibility manifolds
• CONE STRUCTURE OF L²-WASSERSTEIN SPACES
• Characterization of optimal transport plans for the Monge-Kantorovich problem
• Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings
• Optimal Transport

This page was built for publication: A GEOMETRIC STUDY OF WASSERSTEIN SPACES: HADAMARD SPACES