This paper proves W-entropy monotonicity and rigidity for geodesic flow and a Langevin deformation on L^q-Wasserstein spaces over Riemannian manifolds.
Kantorovich, On the translocation of masses
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$W$-entropy formulas and Langevin deformation on the $L^q$-Wasserstein space over Riemannian manifolds
This paper proves W-entropy monotonicity and rigidity for geodesic flow and a Langevin deformation on L^q-Wasserstein spaces over Riemannian manifolds.