Format:
Online-Ressource (Approx. 350 p, online resource)
ISBN:
9788876424298
Series Statement:
Publications of the Scuola Normale Superiore 12
Content:
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
Additional Edition:
ISBN 9788876424281
Additional Edition:
Erscheint auch als Druck-Ausgabe Bellettini, Giovanni, 1963 - Lecture notes on mean curvature flow, barriers and singular perturbations Pisa : Edizioni della Normale, 2013 ISBN 9788876424281
Language:
English
Subjects:
Mathematics
Keywords:
Krümmungsfluss
DOI:
10.1007/978-88-7642-429-8
URL:
Volltext
(lizenzpflichtig)
