Mean Curvature Flow and Isoperimetric Inequalities

Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in pro...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Ritoré, Manuel (Autor), Sinestrari, Carlo (Autor)
Autor Corporativo: SpringerLink (Online service)
Otros Autores: Miquel, Vicente (Editor ), Porti, Joan (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2010.
Edición:1st ed. 2010.
Colección:Advanced Courses in Mathematics - CRM Barcelona,
Temas:
Geometry, Differential.
Global analysis (Mathematics).
Manifolds (Mathematics).
Differential Geometry.
Global Analysis and Analysis on Manifolds.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Formation of Singularities in the Mean Curvature Flow
  • Geometry of hypersurfaces
  • Examples
  • Local existence and formation of singularities
  • Invariance properties
  • Singular behaviour of convex surfaces
  • Convexity estimates
  • Rescaling near a singularity
  • Huisken's monotonicity formula
  • Cylindrical and gradient estimates
  • Mean curvature flow with surgeries
  • Geometric Flows, Isoperimetric Inequalities and Hyperbolic Geometry
  • The classical isoperimetric inequality in Euclidean space
  • Surfaces
  • Higher dimensions
  • Some applications to hyperbolic geometry.

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