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Catalogue Information
Field name	Details
Dewey Class	516.3/62
Title	Ricci flow and the sphere theorem / ([EBook] ) / Simon Brendle.
Author	Brendle, Simon, , 1981-
Publication	Providence, R.I. : : American Mathematical Society, , c2010.
Physical Details	1 online resource (vii, 176 p.)
Series	Graduate studies in mathematics ; 111
ISBN	9781470411732 (online)
Summary Note	"In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's solution of the Poincare conjecture. Furthermore, various convergence theorems have been established. This book provides a concise introduction to the subject as well as a comprehensive account of the convergence theory for the Ricci flow. The proofs rely mostly on maximum principle arguments. Special emphasis is placed on preserved curvature conditions, such as positive isotropic curvature. One of the major consequences of this theory is the Differentiable Sphere Theorem: a compact Riemannian manifold, whose sectional curvatures all lie in the interval (1,4], is diffeomorphic to a spherical space form. This question has a long history, dating back to a seminal paper by H. E. Rauch in 1951, and it was resolved in 2007 by the author and Richard Schoen."--Publisher's description.:
Contents note	Chapter 1. A survey of sphere theorems in geometry: Chapter 2. Hamilton's Ricci flow: Chapter 3. Interior estimates: Chapter 4. Ricci flow on $S 2$: Chapter 5. Pointwise curvature estimates: Chapter 6. Curvature pinching in dimension 3: Chapter 7. Preserved curvature conditions in higher dimensions: Chapter 8. Convergence results in higher dimensions: Chapter 9. Rigidity results: Appendix A. Convergence of evolving metrics: Appendix B. Results from complex linear algebra: Problems:
Mode of acces to digital resource	Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012
Mode of acces to digital resource	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://www.ams.org/gsm/111
See Also	https://doi.org/10.1090/gsm/111
Links to Related Works	Subject References: Ricci flow . Sphere . Authors: Brendle, Simon, 1981- . Series: Graduate studies in mathematics . Classification: 516.3/62 .

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Ricci flow and the sphere theorem /

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