Title: Uniqueness and stability of Ricci flow through singularities,
Abstract: We verify a conjecture of Perelman, which states that there exists a
canonical Ricci flow through singularities starting from an arbitrary compact
Riemannian 3-manifold. Our main result is a uniqueness theorem for such flows,
which, together with an earlier existence theorem of Lott and the second named
author, implies Perelman's conjecture. We also show that this flow through
singularities depends continuously on its initial condition and that it may be
obtained as a limit of Ricci flows with surgery.
Our results have applications to the study of diffeomorphism groups of three
manifolds --- in particular to the Generalized Smale Conjecture --- which will
appear in a subsequent paper.