Lecture Notes on Mean Curvature Flow [recurso electrónico] / by Carlo Mantegazza.
Tipo de material: TextoSeries Progress in Mathematics ; 290Editor: Basel : Springer Basel, 2011Descripción: XII, 168 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783034801454Tema(s): Mathematics | Global analysis (Mathematics) | Mathematics | AnalysisFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 515 Clasificación LoC:QA299.6-433Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA299.6 -433 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 373068-2001 |
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QA299.6 -433 Modern Aspects of the Theory of Partial Differential Equations | QA299.6 -433 Weights, Extrapolation and the Theory of Rubio de Francia | QA299.6 -433 Notions of Positivity and the Geometry of Polynomials | QA299.6 -433 Lecture Notes on Mean Curvature Flow | QA299.6 -433 Spectral Analysis | QA299.6 -433 Mutational Analysis | QA299.6 -433 Value Distribution of Meromorphic Functions |
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.
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