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Hamilton's Ricci Flow
Bennett Chow,Peng Lu,Lei Ni +2 more
TLDR
Riemannian geometry and singularity analysis of Ricci flow have been studied in this paper, where Ricci solitons and special solutions have been used for geometric flows.Abstract:
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 Indexread more
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Notes on Perelman's papers
Bruce Kleiner,John Lott +1 more
TL;DR: In this paper, the Ricci flow with surgery with surgery was shown to die in a finite time, which is the case for the Poincar´ e Conjecture.
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A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow
Huai-Dong Cao,Xi-Ping Zhu +1 more
TL;DR: In this article, a complete proof of the Poincare and geometrization conjectures of Ricci flow is given, based on the accumulative works of many geometric analysts in the past thirty years.
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Rigidity of gradient ricci solitons
Peter Petersen,William Wylie +1 more
TL;DR: In this paper, the authors define a gradient Ricci soliton to be rigid if it is a flat bundle N × GRk where N is the number of vertices in the bundle.
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On the classification of gradient Ricci solitons
Peter Petersen,William Wylie +1 more
TL;DR: In this article, it was shown that the only shrinking gradient solitons with vanishing Weyl tensor and Ricci tensor satisfying a weak integral condition are quotients of the standard ones S n, S n 1 R and R n.
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On Gradient Ricci Solitons with Symmetry
TL;DR: In this paper, it was shown that there are no non-compact cohomogeneity one shrinking gradient Ricci solitons with nonnegative curvature, and that the most symmetry one can expect is an isometric cohomogeneous one group action.