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(Geometric Flows and Geometric Operators) GFO in Pisa

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

speaker: Miles Simon (University of Freiburg)

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 curvature growth of (M,g) is not too extreme. Given such initial data (M,g) we show that a Ricci flow exists for a short time. 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 prove the conjecture of Cheeger-Colding, that such an X must be a manifold.

timetable:
Thu 2 Jul, 11:30 - 12:30, Aula Dini
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