Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces - Memoirs of the American Mathematical Society

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