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.
Polar factorization of maps on R iemannian manifolds
3 Pith papers cite this work. Polarity classification is still indexing.
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Short histories of observations can recover the underlying manifold for transporting discontinuous densities when direct source-target pairs are insufficient due to folds or marginalization.
Proves Monge well-posedness and OT-map regularity for linear-quadratic costs (extending Hindawi-Pomet-Rifford 2011 to non-negative costs) and obtains general entropy interpolation inequalities.
citing papers explorer
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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.
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A geometric approach to the transport of discontinuous densities
Short histories of observations can recover the underlying manifold for transporting discontinuous densities when direct source-target pairs are insufficient due to folds or marginalization.
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Linear quadratic optimal transport and interpolation inequalities
Proves Monge well-posedness and OT-map regularity for linear-quadratic costs (extending Hindawi-Pomet-Rifford 2011 to non-negative costs) and obtains general entropy interpolation inequalities.