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Title: Uniqueness and stability of Ricci flow through singularities
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 3‑manifolds—in particular to the generalized Smale conjecture—which will appear in a subsequent paper.  more » « less
Award ID(s):
2005553
NSF-PAR ID:
10353914
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Acta mathematica
Volume:
228
Issue:
1
ISSN:
1871-2509
Page Range / eLocation ID:
1-215
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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