00000cmm a22000004a 4500 UP-99796217611212389 Buklod 20250120045726.0 m go j cr cn |||aaaaa 250120s2011 nyu||||go||j| ||||||engdd 9783034801454 (eBook) 3034801459 (eBook) 9783034801447 (iLib)UPD-00215704151 CSt DMLR rda eng DMLUC QA 614.82 M36 2011eb Mantegazza, Carlo author Lecture notes on mean curvature flow Carlo Mantegazza. New York Springer 2011 online resource (xii, 166 pages) illustrations text rdacontent computer rdamedia online resource rdacarrier Progress in Mathematics 290 Includes bibliographical references and index 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 Close Curves Appendix F. Important Results without Proof in the Book Bibliography Index IP-based subscription, access limited to within on-campus computer network Access via Electronic Resources of the UPD University Library Website 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 --Provided by publisher Electronic reproduction New York SpringerLink 2011 Available via World Wide Web through SpringerLink Global differential geometry. Differential equations, Parabolic. Flows (Differentiable dynamical systems) Curvature. SpringerLink (Online service). http://link.springer.com/book/10.1007/978-3-0348-0145-4 Available for University of the Philippines Diliman via SpringerLink. Click here to access FO UPD DMLR QA 614.82 M36 2011eb Electronic Resource