Lecture Notes on Mean Curvature Flow

• Main Author: Mantegazza, Carlo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel, 2011.
• Series: Progress in Mathematics ; 290
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Analysis.

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...

Table of Contents:

• 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.