Lecture Notes on Mean Curvature Flow

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...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Mantegazza, Carlo (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Basel : Springer Basel : Imprint: Birkhäuser, 2011.
Édition:1st ed. 2011.
Collection:Progress in Mathematics, 290
Sujets:
Mathematical analysis.
Analysis.
Accès en ligne:Texto Completo
Table des matières:
  • Foreword
  • Chapter 1. Definition and Short Time Existence
  • Chapter 2. Evolution of Geometric Quantities
  • Chapter 3. Monotonicity Formula and Type I Singularities
  • Chapter 4. Type II Singularities
  • Chapter 5. Conclusions and Research Directions
  • Appendix A. Quasilinear Parabolic Equations on Manifolds
  • Appendix B. Interior Estimates of Ecker and Huisken
  • Appendix C. Hamilton's Maximum Principle for Tensors
  • Appendix D. Hamilton's Matrix Li-Yau-Harnack Inequality in Rn
  • Appendix E. Abresch and Langer Classification of Homothetically Shrinking Closed Curves
  • Appendix F. Important Results without Proof in the Book
  • Bibliography
  • Index.

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