Calculus of Variations and Geometric Measure Theory

N. Gigli

On the Heat flow on metric measure spaces: existence, uniqueness and stability

created by gigli on 15 Oct 2009
modified by paolini on 21 Jan 2013


Accepted Paper

Inserted: 15 oct 2009
Last Updated: 21 jan 2013

Journal: Calc. Var. Part. Diff. Eq.
Year: 2010


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