Wasserstein proximal operators are non-expansive under total or 2-base generalized geodesic convexity and locally 1/2-Hölder under ordinary generalized geodesic convexity.
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On the stability of proximal operators in Wasserstein spaces under different notions of convexity
Wasserstein proximal operators are non-expansive under total or 2-base generalized geodesic convexity and locally 1/2-Hölder under ordinary generalized geodesic convexity.