Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations

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 descri...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bellettini, Giovanni (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2013.
Edición:1st ed. 2013.
Colección:Lecture Notes (Scuola Normale Superiore), 12
Temas:
Geometry.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Signed distance from a smooth boundary
  • Mean curvature vector and second fundamental form
  • First variations of volume integrals and of the perimeter
  • Smooth mean curvature flows
  • Huisken's monotonicity formula
  • Inclusion principle. Local well posedness: the approach of Evans-Spruck
  • Grayson's example
  • De Giorgi's barriers
  • Inner and outer regularizations
  • An example of fattening
  • Ilmanen's interposition lemma
  • The avoidance principle
  • Comparison between barriers and a generalized evolution
  • Barriers and level set evolution
  • Parabolic singular perturbations: formal matched asymptotics, convergence and error estimate.

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