Absolutely continuous curves in extended Wasserstein-Orlicz spaces
Stefano Lisini
TL;DR
This paper generalizes the characterization of absolutely continuous curves from Wasserstein spaces to Wasserstein-Orlicz spaces on extended Polish spaces, and explores their geodesic properties.
Contribution
It extends previous results to a broader class of Wasserstein-Orlicz spaces on non-separable extended Polish spaces, providing new insights into their structure.
Findings
Characterization of absolutely continuous curves in Wasserstein-Orlicz spaces
Application to geodesic analysis in these spaces
Extension to non-separable extended Polish spaces
Abstract
In this paper we extend a previous result of the author [Lis07] of characterization of absolutely continuous curves in Wasserstein spaces to a more general class of spaces: the spaces of probability measures endowed with the Wasserstein-Orlicz distance constructed on extended Polish spaces (in general non separable), recently considered in [AGS14]. An application to the geodesics of this Wasserstein-Orlicz space is also given.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Dermatological and Skeletal Disorders