Long-time behavior of 3 dimensional Ricci flow -- Introduction

Abstract

In the following series of papers we analyze the long-time behavior of 3 dimensional Ricci flows with surgery. Our main result will be that if the surgeries are performed correctly, then only finitely many surgeries occur and after some time the curvature is bounded by $C{t}^{-1}$. This result confirms a conjecture of Perelman. In the course of the proof, we also obtain a qualitative description of the geometry as $t\to \infty$.

16 pages, 3 figures

References in corpus (5)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci Flow and the Poincare Conjecture
• Completion of the Proof of the Geometrization Conjecture
• Long-time behavior of 3 dimensional Ricci flow -- Introduction

Cited by in corpus (7)

• Immortal homogeneous Ricci flows
• Ricci flow and contractibility of spaces of metrics
• Long-time behavior of 3 dimensional Ricci flow -- Introduction
• Collapsing in the Einstein flow
• On the long-time behavior of immortal Ricci flows
• Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature
• Convergence of Ricci flow solutions to Taub-NUT