Skip to main content
SpringerLink
Log in
Book cover
  • Textbook
  • © 2013

Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations

Authors:

  1. Giovanni Bellettini

    1. Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 12)

Part of the book sub series: Lecture Notes (Scuola Normale Superiore) (LNSNS)

Sections

Buy it now

eBook USD 19.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 29.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xviii
    PDF

  2. Signed distance from a smooth boundary

    • Giovanni Bellettini
    Pages 1-22

  3. First variations

    • Giovanni Bellettini
    Pages 23-35

  4. Smooth flows

    • Giovanni Bellettini
    Pages 37-58

  5. Huisken’s monotonicity formula

    • Giovanni Bellettini
    Pages 59-68

  6. Inclusion principle

    • Giovanni Bellettini
    Pages 69-84

  8. Local well-posedness: the approach of Evans and Spruck

    • Giovanni Bellettini
    Pages 103-126

  9. Grayson’s example

    • Giovanni Bellettini
    Pages 127-134

  10. De Giorgi’s barriers

    • Giovanni Bellettini
    Pages 135-163

  11. Inner and outer regularizations

    • Giovanni Bellettini
    Pages 165-174

  12. An example of fattening

    • Giovanni Bellettini
    Pages 175-185

  13. Ilmanen’s interposition lemma

    • Giovanni Bellettini
    Pages 187-205

  14. The avoidance principle

    • Giovanni Bellettini
    Pages 207-215

  19. Back Matter

    Pages 297-329
    PDF
Back to top

About this book

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.
Back to top

Keywords

Back to top

Authors and Affiliations

  • Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italia

    Giovanni Bellettini

Back to top

Bibliographic Information

  • Book Title: Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations

  • Authors: Giovanni Bellettini

  • Series Title: Publications of the Scuola Normale Superiore

  • DOI: https://doi.org/10.1007/978-88-7642-429-8

  • Publisher: Edizioni della Normale Pisa

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Edizioni della Normale 2013

  • Softcover ISBN: 978-88-7642-428-1Published: 16 January 2014

  • eBook ISBN: 978-88-7642-429-8Published: 13 May 2014

  • Series ISSN: 2239-1460

  • Series E-ISSN: 2532-1668

  • Edition Number: 1

  • Number of Pages: XVIII, 329

  • Topics: Geometry

Back to top

Publish with us

Policies and ethics

Back to top
Access via your institution

Buy it now

eBook USD 19.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 29.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Search

Navigation