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Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below

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      Abstract

      We consider complete (possibly non-compact) three dimensional Riemannian manifolds (M,g) such that: a) (M,g) is non-collapsed, b) the Ricci curvature of (M,g) is bounded from below, c) the geometry of (M,g) at infinity is not too extreme. Given such initial data (M,g) we show that a Ricci flow exists for a short time interval. This enables us to construct a Ricci flow of any (possibly singular) metric space (X,d) which arises as a Gromov-Hausdorff limit of a sequence of 3-manifolds which satisfy a), b) and c) uniformly. As a corollary we show that such an X must be a manifold.

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      Most cited references 3

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      Deforming the metric on complete Riemannian manifolds

       Wan-Xiong Shi (1989)
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        Ricci flow with surgery on four-manifolds with positive isotropic curvature

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          Complete noncompact three-manifolds with nonnegative Ricci curvature

           Wan-Xiong Shi (1989)
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            Author and article information

            Journal
            2009-03-12
            2009-12-01
            0903.2142

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            Changes: V1 contained an incorrect use of the Hessian comparison theorem (in the section "Conformal deformations ..."). In v2 this is corrected. The condition at infinity for the non-compact case has been modified. There is a short new section:"Previous results". Minor reorganisation
            math.DG math.AP

            Analysis, Geometry & Topology

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