Progress in Mathematics

Lecture Notes on Mean Curvature Flow

Authors: Mantegazza, Carlo

  • detailed and complete introduction to the topic
  • lecture focus: well suited for postgraduate courses
  • summary of the state of the art and open problems
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About this book

This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach (mainly developed by R. Hamilton and G. Huisken). They are well suited for a course at PhD/PostDoc level and can be useful for any researcher interested in a solid introduction to the technical issues of the field. All the proofs are carefully written, often simplified, and contain several comments. Moreover, the author revisited and organized a large amount of material scattered around in literature in the last 25 years.

Reviews

From the book reviews:

“This award-winning monograph provides an introduction to the topic of mean curvature flow of hypersurfaces in Euclidean space for the advanced student and the researcher … . It reorganizes material scattered throughout the literature within the last 25 years, thereby mainly concentrating on the classical parametric approach due to R. Hamilton and G. Huisken.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 174, 2014)

“In the book under review the author mainly discusses some classical results on mean curvature flow of hypersurfaces. … Specifically, the author also gives some recent conclusions, some references to open problems and research directions. The book is not only suitable for beginners but also for researchers.” (Shouwen Fang, Mathematical Reviews, January, 2013)

“This book gives an introduction to the topic of mean curvature flows of hypersurfaces in Euclidean spaces. … It is written in the style of lecture notes and provides a detailed discussion of the classical parametric approach by R. Hamilton and G. Huisken, as well as the results by other authors scattered over the literature of the last 25 years. … The book finishes with 6 appendices.” (Boris S. Kruglikov, Zentralblatt MATH, Vol. 1230, 2012)


Table of contents (5 chapters)

  • Definition and Short Time Existence

    Mantegazza, Carlo

    Pages 1-23

  • Evolution of Geometric Quantities

    Mantegazza, Carlo

    Pages 25-47

  • Monotonicity Formula and Type I Singularities

    Mantegazza, Carlo

    Pages 49-84

  • Type II Singularities

    Mantegazza, Carlo

    Pages 85-114

  • Conclusions and Research Directions

    Mantegazza, Carlo

    Pages 115-122

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0145-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-0348-0144-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-0340-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business 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
Authors
Series Title
Progress in Mathematics
Series Volume
290
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Carlo Mantegazza and Springer Basel AG
eBook ISBN
978-3-0348-0145-4
DOI
10.1007/978-3-0348-0145-4
Hardcover ISBN
978-3-0348-0144-7
Softcover ISBN
978-3-0348-0340-3
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XII, 168
Topics