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September 19, 2025Advances in Calculus of Variations

On nonexpansiveness of metric projection operators on Wasserstein spaces

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Authors

AAAnshul AdveAMAlpár R. Mészáros

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Overview

This paper reveals properties of metric projections on Wasserstein spaces, suggesting implications for convex subsets.

Key Points

  • Wasserstein spaces exhibit nonexpansiveness of metric projections in certain conditions, enhancing geometric understanding.
  • When dealing with d=1, corresponding projection operators are nonexpansive, yet issues arise with dimensions greater than 1.
  • Use of intrinsic analysis establishes nonexpansiveness and curvature properties in Wasserstein spaces for d≥2 with bounded probability measures.
  • The analysis shows Wasserstein spaces do not locally satisfy the projection criterion, suggesting deeper structural implications.

Cite This Study

Adve et al. (2025) studied this question.

synapsesocial.com/papers/68d464ea31b076d99fa63ec9https://doi.org/10.1515/acv-2024-0112
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