Gradient Flows : in Metric Spaces and in the Space of Probability Measures

Chapter 1 Introduction

Chapter 3 Curves and Gradients in Metric Spaces

Chapter 4 Existence of Curves of Maximal Slope and their Variational Approximation

Chapter 5 Proofs of the Convergence Theorems

Chapter 6 Uniqueness, Generation of Contraction Semigroups, Error Estimates

Chapter 7 Preliminary Results on Measure Theory

Chapter 8 The Optimal Transportation Problem

Chapter 9 The Wasserstein Distance and its Behaviour along Geodesics

Chapter 10 Absolutely Continuous Curves in P p ( X ) and the Continuity Equation

Chapter 11 Convex Functionals in P p ( X )

Chapter 12 Metric Slope and Subdifferential Calculus in P p ( X )

Chapter 13 Gradient Flows and Curves of Maximal Slope in P p ( X )