$W$-entropy formulas and Langevin deformation on the $L^q$-Wasserstein space over Riemannian manifolds

Rong Lei, Xiang-Dong Li, Yu-Zhao Wang

We first prove the $W$-entropy formula and rigidity theorem for the geodesic flow on the $L^q$-Wasserstein space over a complete Riemannian manifold with bounded geometry condition…