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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2012, Issue 662


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

Miles Simon


We consider complete (possibly non-compact) three dimensional Riemannian manifolds (M, g) such that: (a) (M, g) is non-collapsed (i.e. the volume of an arbitrary ball of radius one is bounded from below by v > 0), (b) the Ricci curvature of (M, g) is bounded from below by k, (c) the geometry at infinity of (M, g) is not too extreme (or (M, g) is compact). Given such initial data (M, g) we show that a Ricci flow exists for a short time interval 0, T), where T T(v, k) > 0. This enables us to construct a Ricci flow of any (possibly singular) metric space (X, d) which arises as a GromovHausdorff (GH) 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. This shows that the conjecture of M. AndersonJ. CheegerT. ColdingG. Tian is correct in dimension three.

About the article

Received: 2009-11-17

Revised: 2009-12-01

Published in Print: 2012-01-01

Citation Information: Journal fr die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 662, Pages 59–94, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2011.088.

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