Inserted: 15 oct 2009
Last Updated: 21 jan 2013
Journal: Calc. Var. Part. Diff. Eq.
We prove existence and uniqueness of the gradient flow of the Entropy functional under the only assumption that this functional is $\lambda$-geodesically convex for some $\lambda\in\mathbb R$ and lower semicontinuous. Also, we prove a general stability result for gradient flows of geodesically convex functionals which $\Gamma-$converge to some limit functional. Such stability result applies directly to the case of the Entropy functional on compact spaces.
Keywords: entropy, Gradient Flow, Ricci bound