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001 ocn436866951;

003 OCoLC;

005 20141212074830.0;

008 090914s2010 riu b 001 0 eng ;

010 a| 2009037261;

020 a| 9780821849385 (hardcover : alk. paper);

020 a| 0821849387 (hardcover : alk. paper);

029 1 a| CDXb| 10785893;

029 1 a| DEBBGb| BV035971426;

029 1 a| AU@b| 000044659581;

029 1 a| NZ1b| 13327988;

029 1 a| NLGGCb| 326131221;

029 1 a| HEBISb| 227290003;

035 a| (Sirsi) o436866951;

035 a| (OCoLC)436866951;

049 a| EREE;

050 00 a| QA377.3b| .B74 2010;

082 00 a| 516.3/622| 22;

084 a| SK 3702| rvk;

084 a| 31.522| bcl;

084 a| 31.552| bcl;

084 a| 31.452| bcl;

100 1 a| Brendle, Simon,d| 1981-=| ^A1060746;

245 10 a| Ricci flow and the sphere theorem /c| Simon Brendle.;

300 a| vii, 176 pages ;c| 27 cm.;

336 a| text2| rdacontent;

337 a| unmediated2| rdamedia;

338 a| volume2| rdacarrier;

490 1 a| Graduate studies in mathematics ;v| v. 111;

504 a| Includes bibliographical references and index.;

505 0 a| A survey of sphere theorems in geometry -- Hamilton's Ricci flow -- Interior estimates -- Ricci flow on S2 -- Pointwise curvature estimates -- Curvature pinching in dimension 3 -- Preserved curvature conditions in higher dimensions -- Convergence results in higher dimensions -- Rigidity results.;

520 a| "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.;

650 0 a| Ricci flow.=| ^A704224;

650 0 a| Sphere.=| ^A104516;

830 0 a| Graduate studies in mathematicsv| v. 111.=| ^A347883;

856 u| http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018865429&line_number=0001&func_code=DB_RECORDS&service_type=MEDIAz| Inhaltsverzeichnis;

949 a| QA377.3 .B74 2010h| JOYNER48o| jmpli| 30372015830935;

938 a| YBP Library Servicesb| YANKn| 3135210;

938 a| Blackwell Book Serviceb| BBUSn| R6830004c| $47.00;

938 a| Coutts Information Servicesb| COUTn| 10785893;

994 a| C0b| ERE;

596 a| 1;

998 a| 2654683;

999 a| QA377.3 .B74 2010w| LCc| 1i| 30372015830935d| 4/8/2013e| 1/18/2012f| 4/8/2013g| 2l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 1/9/2012x| BOOKz| JSTACKSo| .STAFF. jmpl;

Ricci flow and the sphere theorem / Simon Brendle.

Author/creator	Brendle, Simon, 1981-
Format	Book
Publication Info	Providence, R.I. : American Mathematical Society, ©2010.
Description	vii, 176 pages ; 27 cm.
Subjects	Ricci flow. Sphere.

Series	Graduate studies in mathematics ; v. 111 Graduate studies in mathematics v. 111. ^A347883
Contents	A survey of sphere theorems in geometry -- Hamilton's Ricci flow -- Interior estimates -- Ricci flow on S2 -- Pointwise curvature estimates -- Curvature pinching in dimension 3 -- Preserved curvature conditions in higher dimensions -- Convergence results in higher dimensions -- Rigidity results.
Abstract	"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.
Bibliography note	Includes bibliographical references and index.
LCCN	2009037261
ISBN	9780821849385 (hardcover : alk. paper)
ISBN	0821849387 (hardcover : alk. paper)

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Ricci flow and the sphere theorem / Simon Brendle.

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