Böcker av Luigi Ambrosio

This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport.

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.

In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others.

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively.