Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
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Perelman establishes finite extinction for the relevant three-manifold class under Ricci flow with surgery; the simply connected closed case is used in the Poincaré proof.
Passage ID: poincare-conjecture:entry:extinction:v1
Source item: Abstract; finite-extinction argument
Source record: perelman-extinction@arxiv-math-0307245v1
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Problem publication v13
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Proved
Established result in cited source
Extinction concerns the flow with surgery, including discarded components; it does not mean that the original manifold vanishes under a homeomorphism.
Observed Oct 12, 2026
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Recorded authorship
Grigori Perelman
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Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
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