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

Miles Simon

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arXiv · 0903.2142

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

Miles Simon

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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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Miles Simon. 2009-03-12. Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below. https://arxiv.org/abs/0903.2142

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