Lecture Notes (Scuola Normale Superiore)

Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations

Authors: Bellettini, Giovanni

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  • 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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eBook 18,18 €
price for Spain (gross)
  • ISBN 978-88-7642-429-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Softcover 24,96 €
price for Spain (gross)
  • ISBN 978-88-7642-428-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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)

Table of contents (17 chapters)
  • Signed distance from a smooth boundary

    Pages 1-22

    Bellettini, Giovanni

  • First variations

    Pages 23-35

    Bellettini, Giovanni

  • Smooth flows

    Pages 37-58

    Bellettini, Giovanni

  • Huisken’s monotonicity formula

    Pages 59-68

    Bellettini, Giovanni

  • Inclusion principle

    Pages 69-84

    Bellettini, Giovanni

Buy this book

eBook 18,18 €
price for Spain (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 24,96 €
price for Spain (gross)
  • ISBN 978-88-7642-428-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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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
Number of Pages
XVIII, 329
Topics