Calculus of Variations and Geometric Measure Theory
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G. Bellettini

Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations

created by belletti on 09 Dec 2014



Inserted: 9 dec 2014

Journal: Edizioni della Scuola Normale
Pages: xviii-329
Year: 2013


The aim of this book is to give an introduction to mean curvature flow using, as much as possible, a parametrization free approach. Some relevant aspects of mean flow are described, such as the role of the signed distance function and the comparison principle, and their use in the theory of barriers. 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 parabolic Allen-Cahn's equation to mean curvature flow for sufficiently short times, together with an error estimate.

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