This is an expository paper on the theory of gradient flows, and in particular of those PDEs
which can be interpreted as gradient flows for the Wasserstein metric on the space of …

Why a new book on optimal transport? Were the two books by Fields Medalist Cédric Villani
not enough? And what about the Bible of Gradient Flows, the book by Luigi Ambrosio …

Analysis on metric spaces emerged in the 1990s as an independent research field providing
a unified treatment of first-order analysis in diverse and potentially nonsmooth settings …

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

This book is about differentiation of functions. It is divided into two parts, which can be used
as different textbooks, one for an advanced undergraduate course in functions of one …

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff
distance which have the goal of modeling and tackling the practical problems of object …

The $ p $-Laplace equation is the main prototype for nonlinear elliptic problems and forms a
basis for various applications, such as injection moulding of plastics, nonlinear elasticity …

We introduce and analyze lower (Ricci) curvature bounds Curv\left(M,d,m\right)⩾ K for metric
measure spaces \left(M,d,m\right). Our definition is based on convexity properties of the …

This second edition takes advantage of several comments received by colleagues and
students. With respect to the first edition (published by SIAM in 2006) several new sections …

We introduce a curvature-dimension condition CD (K, N) for metric measure spaces. It is
more restrictive than the curvature bound Curv\left(M,d,m\right)>K (introduced in Sturm KT …