Lecture Notes (Scuola Normale Superiore)

Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations

Authors: Bellettini, Giovanni

  • Elementary introduction to mean curvature flow, including the short time existence result, using the signed distance function
  • Detailed study of minimal barriers and their regularizations for mean curvature flow
  • An example of fattening
  • Convergence and error estimate for the parabolic Allen-Cahn equation
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About this Textbook

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.

Table of contents (17 chapters)

Buy this book

eBook $19.99
price for USA (gross)
  • ISBN 978-88-7642-429-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $29.99
price for USA
  • ISBN 978-88-7642-428-1
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations
Authors
Series Title
Lecture Notes (Scuola Normale Superiore)
Series Volume
12
Copyright
2013
Publisher
Edizioni della Normale
Copyright Holder
Edizioni della Normale
eBook ISBN
978-88-7642-429-8
DOI
10.1007/978-88-7642-429-8
Softcover ISBN
978-88-7642-428-1
Edition Number
1
Topics