Collapsing Three-Manifolds Under a Lower Curvature Bound

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Perelman???s Stability Theorem (2007, background): “However, as was communicated to the author by Kleiner, for that particular application, if one traces through the proofs of [26, 27] carrying along the additional bounds arising from the Ricci flow, then one finds that in each instance when a 3-dimensional Alexandrov space arises as a Gromov-Hausdor”
Recent progress on the Poincaré conjecture and the classification of 3-manifolds (2004, background): “For results on collapsing metrics with lower curvature bound, see for example [22] and [23].”
Completion of the Proof of the Geometrization Conjecture (2008, background): “ional limits. We need this result in order to handle sequences of points x∈ Mn converging to a singular point of a 2-dimensional limit. The following is a reformulation in our context of Lemma 3.6 of [22]. Proposition 2.26. For any δ>0, the following holds for all µ>0 suﬃciently small. Fix r&g”