Descrizione

The aim of this book is to give an introduction to mean curvature flow using, as much as possible, a parameter-free approach. Some relevant aspects of mean curvature flow are illustrated, such as the role of the signed distance function and the comparison principle, and their use in the theory of minimal barriers is explained. Some simple examples of singularities are discussed. Finally, also making use of a formal asymptotic inner and outer expansion, we prove the convergence of the singularly perturbed parabolic Allen-Cahn equation to mean curvature flow for sufficiently short times, and provide an error estimate.