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. Hamiltonand 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. Detailed and complete introduction to the topic. lecture focus: well suited for postgraduate courses. Summary of the state of the art and open problems. INDICE: Foreword. Chapter 1. Definition and Short Time Existence. Chapter 2. Evolution of Geometric Quantities. Chapter 3. Monotonicity Formula and TypeI Singularities. Chapter 4. Type II Singularities. Chapter 5. Conclusions andResearch 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.
- ISBN: 978-3-0348-0144-7
- Editorial: Springer Basel
- Encuadernacion: Cartoné
- Páginas: 124
- Fecha Publicación: 30/06/2011
- Nº Volúmenes: 1
- Idioma: Inglés