Establishes an explicit strong-convexity modulus for the barycentric variance functional on Alexandrov spaces, implying Hölder stability of barycenters and empirical consistency bounds without using linear structure.
Barycenters in A lesxandrov spaces of curvature bounded below
2 Pith papers cite this work. Polarity classification is still indexing.
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Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
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Quantitative Stability of Wasserstein Barycenters over Alexandrov Spaces with Lower Curvature Bounds
Establishes an explicit strong-convexity modulus for the barycentric variance functional on Alexandrov spaces, implying Hölder stability of barycenters and empirical consistency bounds without using linear structure.
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Absolute continuity of generalized Wasserstein barycenters of finitely many measures
Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.