Hamilton's Ricci Flow
Seiten
2007
American Mathematical Society (Verlag)
978-0-8218-4231-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4231-7 (ISBN)
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Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book introduces Ricci flow for graduate students and mathematicians interested in working in the subject. It reviews the relevant basics of Riemannian geometry. It also introduces some general methods of geometric analysis and other geometric flows.
Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincare conjecture and Thurston's geometrization conjecture.
Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincare conjecture and Thurston's geometrization conjecture.
Riemannian geometry Fundamentals of the Ricci flow equation Closed 3-manifolds with positive Ricci curvature Ricci solitons and special solutions Isoperimetric estimates and no local collapsing Preparation for singularity analysis High-dimensional and noncompact Ricci flow Singularity analysis Ancient solutions Differential Harnack estimates Space-time geometry Appendix A. Geometric analysis related to Ricci flow Appendix B. Analytic techniques for geometric flows Appendix S. Solutions to selected exercises Bibliography Index.
| Erscheint lt. Verlag | 1.1.2007 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 1301 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-4231-5 / 0821842315 |
| ISBN-13 | 978-0-8218-4231-7 / 9780821842317 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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