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.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
Graduate Studies in Mathematics |
Release date: |
2006 |
Authors: |
Bennett Chow
• Peng Lu
• Lei Ni
|
Pages: |
608 |
ISBN-13: |
978-1-4704-7369-3 |
Categories: |
Books
|
LSN: |
1-4704-7369-0 |
Barcode: |
9781470473693 |
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!