Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature
نویسنده
چکیده
In this paper we study the Ricci flow on compact four-manifolds with positive isotropic curvature and with no essential incompressible space form. Our purpose is two-fold. One is to give a complete proof of the main theorem of Hamilton in [17]; the other is to extend some results of Perelman [26], [27] to four-manifolds. During the the proof we have actually provided, up to slight modifications, all necessary details for the part from Section 1 to Section 5 of Perelman’s second paper [27] on the Ricci flow. We also establish a uniqueness theorem for the Ricci flow on complete noncompact manifolds.
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