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Ricci Flow and the Poincaré Conjecture
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Morgan and Tian give a detailed proof of Perelman’s result, using Ricci flow with surgery and finite-time extinction to obtain the three-sphere conclusion.
Passage ID: poincare-conjecture:entry:proof:v1
Source item: Clay monograph 3; introduction, Theorem 0.1 and Corollary 0.2
Source record: morgan-tian-poincare@clay-monograph-3-2007
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Problem publication v13
Source assessment
Proved
Established result in cited source
Smoothness is additional structure; in dimension three the classification agrees with the topological theorem via smoothing and uniqueness of smooth structures.
Observed Oct 12, 2026
Scope
The smooth three-dimensional theorem
Scope
The topological three-dimensional Poincaré theorem
History
A detailed proof account
Question
Poincaré conjecture
Recorded authorship
John Morgan · Gang Tian
John Morgan; Gang Tian
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Ricci Flow and the Poincaré Conjecture
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