Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations (BOK)

Giovanni Bellettini

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The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen-Cahn (or Ginsburg-Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.


Språk Engelsk Engelsk Innbinding Heftet
Utgitt 2013 Forfatter Giovanni Bellettini
ISBN 9788876424281
Antall sider 350 Dimensjoner 15,5cm x 23,5cm x 2,3cm
Vekt 680 gram Emner og form Geometry