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Ricci flow with surgery on three-manifolds
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In this article, the Ricci flow with surgeries was constructed, and a lower bound on the volume of maximal horns and the smoothness of solutions was established. But this lower bound was later shown to be unjustified and irrelevant for the other conclusions.Abstract:
This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-print: the exceptions are (1) the statement that manifolds that can collapse with local lower bound on sectional curvature are graph manifolds - this is deferred to a separate paper, since the proof has nothing to do with the Ricci flow, and (2) the claim on the lower bound for the volume of maximal horns and the smoothness of solutions from some time on, which turned out to be unjustified and, on the other hand, irrelevant for the other conclusions.read more
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References
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The entropy formula for the Ricci flow and its geometric applications
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Three-manifolds with positive Ricci curvature
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The Harnack estimate for the Ricci flow
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Collapsing riemannian manifolds while keeping their curvature bounded. I.
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Four-manifolds with positive isotropic curvature
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