The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between diffe

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

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 meas

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential