Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations

Giovanni Bellettini

ISBN 10: 8876424288 / ISBN 13: 9788876424281

Verlag: Scuola Normale Superiore, 2014

Beschreibung

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9788876424281

Bibliografische Details

• Titel: Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations
• Verlag: Scuola Normale Superiore
• Erscheinungsjahr: 2014
• Sprache: Englisch
• ISBN-10: 8876424288
• ISBN-13: 9788876424281
• Einband: Taschenbuch
• Zustand: Neu

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Inhaltsangabe

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.