Barycenters in Alexandrov spaces of curvature bounded below

DOI10.1515/advgeom-2011-058zbMath1276.53073OpenAlexW2036352886MaRDI QIDQ4910045

Shin-Ichi Ohta

Publication date: 25 March 2013

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/d3e15d842d9f97ff3d8baa4de9d9290d423a26a6

zbMATH Keywords

Alexandrov spacebarycenterWasserstein spacevariance inequality

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

Related Items (14)

Existence and consistency of Wasserstein barycenters ⋮ Geometric Averages of Partitioned Datasets ⋮ Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics ⋮ Fréchet single index models for object response regression ⋮ Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space ⋮ Distances and isomorphism between networks: stability and convergence of network invariants ⋮ A rigidity theorem in Alexandrov spaces with lower curvature bound ⋮ Jensen's inequality on convex spaces ⋮ Fréchet means for distributions of persistence diagrams ⋮ Discrete-time gradient flows and law of large numbers in Alexandrov spaces ⋮ On the measure of the cut locus of a Fréchet mean ⋮ A note on flatness of non separable tangent cone at a barycenter ⋮ Nonparametric regression in nonstandard spaces ⋮ Stability of the cut locus and a central limit theorem for Fréchet means of Riemannian manifolds

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