Notes and commentary on Perelman's Ricci flow papers

Introduction

This webpage is meant to be a repository for material related to Perelman's papers on Ricci flow.   Please email any contributions, comments or corrections to bkleiner@cims.nyu.edu or lott@math.berkeley.edu.

The page is organized as
1. Source material
2. Lecture notes
3. Background on the geometrization conjecture
4. Background on Ricci flow and geometrization
5. Overviews of Perelman's papers
6. Detailed notes and commentary on Perelman's papers

We do not take responsibility for the mathematical accuracy of anything posted here.
 

Bruce Kleiner and John Lott
 


Source material

``The entropy formula for the Ricci flow and its geometric applications'' by Grisha Perelman   arXiv link

``Ricci flow with surgery on three-manifolds'' by Grisha Perelman   arXiv link

``Finite extinction time for the solutions to the Ricci flow on certain three-manifolds'' by Grisha Perelman   arXiv link

``Volume collapsed three-manifolds with a lower curvature bound'' by Takashi Shioya and Takao Yamaguchi   arXiv link journal link

``Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman'' by Toby Colding and Bill Minicozzi   arXiv link journal link

``Width and finite extinction time of Ricci flow'' by Toby Colding and Bill Minicozzi   arXiv link journal link

``Collapsing irreducible 3-manifolds with nontrivial fundamental group'' by Laurent Bessieres, Gerard Besson, Michel Boileau and Sylvain Maillot   arXiv link journal link

``Completion of the proof of the geometrization conjecture'' by John Morgan and Gang Tian   arXiv link

``Locally collapsed 3-manifolds'' by Bruce Kleiner and John Lott   arXiv link


Lecture notes

Christina Sormani's notes on the first week of Perelman's Stony Brook lectures   webpage link

Yair Minsky's notes on Perelman's Stony Brook lectures   pdf


Background on the geometrization conjecture

``Towards the Poincare conjecture and the classification of 3-manifolds'' by Jack Milnor   journal link

``Geometrization conjecture and Ricci flow'' by Misha Kapovich   webpage link


Background on Ricci flow and geometrization

``Lectures on the Ricci flow'' by Peter Topping,   webpage link

``Recent developments on the Ricci flow'' by Ben Chow and Huai-Dong Cao,  arXiv link journal link


Overviews of Perelman's papers

``Geometrization of 3-manifolds via the Ricci flow'' by Mike Anderson   journal link

``Recent progress on the Poincare conjecture and the classification of 3-manifolds'' by John Morgan   journal link

``Preuve de la conjecture de Poincare en deformant la metrique par la courbure de Ricci, d'apres G. Perelman'' by Gerard Besson, Seminaire Bourbaki #947 of June 26, 2005    pdf


Detailed notes and commentary on Perelman's papers

``Notes on Perelman's papers'' by Bruce Kleiner and John Lott   arXiv link journal link

``Ricci flow and the Poincare conjecture'' by John Morgan and Gang Tian   arXiv link book link

``Geometrisation of 3-manifolds'' by Laurent Bessieres, Gerard Besson, Michel Boileau, Sylvain Maillot and Joan Porti   book link

``Curvature formulas in Section 6.1 of Perelman's paper", by Guofang Wei    webpage link

``On the l-function and the reduced volume of Perelman", by Rugang Ye    webpage link

``On the uniqueness of 2-dimensional kappa-Solutions", by Rugang Ye  webpage link

``Remarks on Perelman's papers'' by Mike Anderson   webpage link

``Uniqueness of standard solutions in the work of Perelman'' by Peng Lu and Gang Tian   pdf

``Uniqueness of the Ricci flow on complete noncompact manifolds'' by Bing-Long Chen and Xi-Ping Zhu,   arXiv link journal link

``A note on Perelman's LYH inequality'' by Lei Ni,   arXiv link journal link

``Notes on Perelman's second paper'' by Yu Ding   webpage link

``Bounding scalar curvature and diameter along the Kaehler-Ricci flow (after Perelman) and some applications'' by Natasa Sesum and Gang Tian   ps  dvi  pdf



 
 

This material is based upon work supported by the National Science Foundation under grants DMS-0204506, DMS-0306242 and DMS-0505610. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.