A Self‐Dual Polar Factorization for Vector Fields

Abstract

We establish a self-dual version of Brenier's polar decomposition for non-degenerate vector fieldswhere S is a self-dual ("almost idempotent") measure preserving point transformation on Ω, and H : R N × R N → R is a globally Lipschitz anti-symmetric convex-concave Hamiltonian. Just like Brenier's polar decomposition, our representation unifies several seemingly unrelated classical results.

The Roommate Problem: Is More Stable than You Think

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Continuity and Estimates for Multimarginal Optimal Transportation Problems with Singular Costs

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