Long-time behavior of 3 dimensional Ricci flow -- D: Proof of the main results

Abstract

This is the fourth and last part of a series of papers on the long-time behavior of 3 dimensional Ricci flows with surgery. In this paper, we prove our main two results. The first result states that if the surgeries are performed correctly, then the flow becomes non-singular eventually and the curvature is bounded by $C{t}^{-1}$. The second result provides a qualitative description of the geometry as $t\to \infty$.

100 pages, 15 figures, revised version

References in corpus (1)

• A simple proof of Perelman's collapsing theorem for 3-manifolds

Cited by in corpus (2)

• O(2)-symmetry of 3D steady gradient Ricci solitons
• Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature