# Notes on Perelman's papers

@article{Kleiner2006NotesOP,
title={Notes on Perelman's papers},
author={Bruce Kleiner and John Lott},
journal={arXiv: Differential Geometry},
year={2006}
}
• Published 2006
• Mathematics
• arXiv: Differential Geometry
These are detailed notes on Perelman's papers "The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds".
497 Citations
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#### References

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A note on Perelman’s LYH inequality
We give a proof to the Li-Yau-Hamilton type inequality claimed by Perelman on the fundamental solution to the conjugate heat equation. The rest of the paper is devoted to improving the knownExpand
A NOTE ON PERELMAN’S LYH TYPE INEQUALITY
• 2006
We give a proof to the Li-Yau-Hamilton type inequality claimed by Perelman on the fundamental solution to the conjugate heat equation. The rest of the paper is devoted to improving the knownExpand
A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow
• Mathematics
• 2006
In this paper, we give a complete proof of the Poincare and the geometrization conjectures. This work depends on the accumulative works of many geometric analysts in the past thirty years. This proofExpand
On the l-Function and the Reduced volume of Perelman II
The main purpose of this paper is to present a number of analytic and geometric properties of the l-function and the reduced volume of Perelman, including in particular the monotonicity, the upperExpand
Perelman???s Stability Theorem
We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence Xi of Alexandrov spaces with curv > k Gromov-Hausdorff converging to a compact AlexandrovExpand
Perelman’s invariant, Ricci flow, and the Yamabe invariants of smooth manifolds
• Mathematics
• 2006
Abstract.In his study of Ricci flow, Perelman introduced a smooth-manifold invariant called $$\bar{\lambda}$$. We show here that, for completely elementary reasons, this invariant simply equals theExpand
The Ricci Flow: An Introduction
• Mathematics
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The Ricci flow of special geometries Special and limit solutions Short time existence Maximum principles The Ricci flow on surfaces Three-manifolds of positive Ricci curvature Derivative estimatesExpand
Scalar curvature and the existence of geometric structures on 3-manifolds, II
This paper analyses the convergence and degeneration of sequences of metrics on a 3-manifold, and relations of such with Thurston's geometrization conjecture. The sequences are minimizing sequencesExpand
RECENT DEVELOPMENTS ON THE RICCI FLOW
• Mathematics
• 1998
This article reports recent developments of the research on Hamilton's Ricci flow and its applications.
Lectures on the Ricci Flow
1. Introduction 2. Riemannian geometry background 3. The maximum principle 4. Comments on existence theory for parabolic PDE 5. Existence theory for the Ricci flow 6. Ricci flow as a gradient flow 7.Expand