# 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 25 May 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".
515 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 known

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• 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 known

### 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 upper

### 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 Alexandrov

### Perelman’s invariant, Ricci flow, and the Yamabe invariants of smooth manifolds

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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 the

### 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 sequences

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• Art
• 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.

### Volume collapsed three-manifolds with a lower curvature bound

• Mathematics
• 2003
In this paper we determine the topology of three-dimensional complete orientable Riemannian manifolds with a uniform lower bound of sectional curvature whose volume is sufficiently small.

### Algorithmic Topology and Classification of 3-Manifolds

Simple and special polyhedra.- Complexity theory of 3-manifolds.- Haken theory of normal surfaces.- Applications of the theory of normal surfaces.- Algorithmic recognition of S3.- Classification of