Böcker av Giuseppe Savare

Provides new characterizations of the curvature dimension condition in the context of metric measure spaces $(X,\mathsf d,\mathfrak m)$. The authors' approach takes into account suitable weighted action functionals, and uses the nonlinear diffusion semigroup induced by the $N$-dimensional entropy, in place of the heat flow

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion.