Lecture notes on mean curvature flow barriers and singular perturbations by Giovanni Bellettini

Format:

Book

Author/Creator:

Bellettini, Giovanni, author.

Contributor:

Scuola normale superiore (Italy)

Series:

Appunti 12

Appunti / Scuola Normale Superiore 12

Language:

English

Subjects (All):

Curvature.

Flows (Differentiable dynamical systems).

Physical Description:

1 online resource

Place of Publication:

Pisa Della Normale 2013

System Details:

text file

PDF

Summary:

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 AllenCahn (or GinsburgLandau) 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

Contents:

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 Huiskens monotonicity formula Inclusion principle. Local well posedness: the approach of EvansSpruck Graysons example De Giorgis barriers Inner and outer regularizations An example of fattening Ilmanens 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

Notes:

Print version record

Other Format:

Print version Bellettini, Giovanni. Lecture notes on mean curvature flow

ISBN:

9788876424298

8876424296

OCLC:

880372264

Access Restriction:

Restricted for use by site license