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＜電子ブック＞
Lecture Notes on Mean Curvature Flow / by Carlo Mantegazza
(Progress in Mathematics. ISSN:2296505X ; 290)

版	1st ed. 2011.
出版者	(Basel : Springer Basel : Imprint: Birkhäuser)
出版年	2011
本文言語	英語
大きさ	XII, 168 p : online resource
著者標目	*Mantegazza, Carlo author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis FREE:Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-0348-0145-4

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