The heat equation on manifolds as a gradient flow in the Wasserstein space (Q974765)

The author considers the gradient flow of the relative entropy functional in the Wasserstein space \(P(M)\) of probability measures defined on the Riemannian manifold \(M\). In particular, a Riemannian structure on \(P(M)\) is introduced, by assuming the Ricci curvature of the manifold to be bounded below, the classical minimizing movements scheme is considered (existence) and the contractivity of the flow (uniqueness) is proved.