Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below
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.
Keywords
Cite
@article{arxiv.0903.2142,
title = {Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below},
author = {Miles Simon},
journal= {arXiv preprint arXiv:0903.2142},
year = {2009}
}
Comments
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