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}
}
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". 
PERELMAN'S PROOF OF THE POINCAR´ E CONJECTURE: A NONLINEAR PDE PERSPECTIVE
We discuss some of the key ideas of Perelman's proof of Poincare's conjecture via the Hamilton program of using the Ricci flow, from the perspec- tive of the modern theory of nonlinear partialExpand
Hyperbolic thermostat and Hamilton's Harnack inequality for the Ricci flow
In this paper, we will recover Hamilton's Harnack inequality for the Ricci flow from the view point of Hyperbolic thermostat.
Perelman's reduced volume and a gap theorem for the Ricci flow
In this paper, we show that any ancient solution to the Ricci flow with the reduced volume whose asymptotic limit is sufficiently close to that of the Gaussian soliton is isometric to the EuclideanExpand
Some Elementary Consequences of Perelman’s Canonical Neighborhood Theorem
In this purely expository note, we deduce a few known direct consequences of Perelman’s canonical neighborhood theorem for 3-dimensional Ricci flow and compactness theorem for 3-dimensionalExpand
A Simple Proof On Poincar\'e Conjecture
We give a simple proof on the Poincar\'e's conjecture which states that every compact smooth $3-$manifold which is homotopically equivalent to $S^3$ is diffeomorphic to $S^3$.
A note on the Hitchin-Thorpe inequality and Ricci flow on 4-manifolds
In this short paper, we prove a Hitchin-Thorpe type inequality for closed 4-manifolds with non-positive Yamabe invariant, and admitting long time solutions of the normalized Ricci flow equation withExpand
Relative volume comparison of Ricci flow
In this paper we derive a relative volume comparison of Ricci flow under a certain local curvature condition. It is a refinement of Perelman’s no local collapsing theorem in Perelman (2002).
Relative volume comparison of Ricci Flow and its applications
In this paper, we derive a relative volume comparison estimate along Ricci flow and apply it to studying the Gromov-Hausdorff convergence of K\"ahler-Ricci flow on a minimal manifold. This newExpand
Optimal transport and Perelman’s reduced volume
We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman’s reduced volume.
Perelman, Poincare, and the Ricci Flow
In this expository article, we introduce the topological ideas and context central to the Poincare Conjecture. Our account is intended for a general audience, providing intuitive definitions andExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 80 REFERENCES
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
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
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
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
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
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
...
1
2
3
4
5
...