Surgical Ricci Flow on Four-Manifolds with Positive Isotropic Curvature

摘要

In this article we report our recent works [1] and [2] on the Ricci flow We extended Perelman's singularity characterization of the three-dimensional Ricci flow to four-dimensional manifolds with positive isotropic curvature and gave a complete proof for the main theorem of Hamilton in [7], We also established a uniqueness result for the solutions of the Ricci flow on complete noncompact manifolds.