"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds"
E684915
"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds" is a landmark mathematical paper by Grigori Perelman that advances the analysis of Ricci flow in three dimensions and plays a key role in his proof of the Poincaré conjecture.
Observed surface forms (1)
| Surface form | Occurrences |
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| Finite extinction time for the solutions to the Ricci flow on certain three-manifolds | 0 |
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical paper
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research article ⓘ |
| archive | arXiv NERFINISHED ⓘ |
| arXivCategory | math.DG ⓘ |
| associatedConjecture |
Poincaré conjecture
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Thurston geometrization conjecture NERFINISHED ⓘ |
| author | Grigori Perelman NERFINISHED ⓘ |
| authorFullName | Grigori Yakovlevich Perelman NERFINISHED ⓘ |
| buildsOn | Richard S. Hamilton's work on Ricci flow ⓘ |
| citationForm | Perelman, G. "Finite extinction time for the solutions to the Ricci flow on certain three-manifolds." arXiv preprint math/0307245. ⓘ |
| contributionTo |
proof of the Poincaré conjecture
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proof of the geometrization conjecture ⓘ |
| countryOfAuthor | Russia NERFINISHED ⓘ |
| decade | 2000s ⓘ |
| era | early 21st century mathematics ⓘ |
| field |
Riemannian geometry
NERFINISHED
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differential geometry ⓘ geometric analysis ⓘ |
| focusesOn |
finite extinction time of Ricci flow solutions
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three-dimensional manifolds with certain curvature conditions ⓘ |
| impact | considered a landmark in geometric analysis ⓘ |
| influenced |
research on geometric flows
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subsequent work on three-dimensional Ricci flow ⓘ |
| language | English ⓘ |
| mainTopic |
Poincaré conjecture
NERFINISHED
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Ricci flow ⓘ geometrization conjecture NERFINISHED ⓘ three-manifolds ⓘ |
| mathematicsSubject |
3-manifold topology
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global analysis ⓘ |
| partOfSeries | Perelman's Ricci flow papers NERFINISHED ⓘ |
| proves | finite-time extinction for Ricci flow on certain three-manifolds ⓘ |
| provesPropertyOf | Ricci flow on certain three-manifolds ⓘ |
| publishedAs | arXiv preprint ⓘ |
| relatedWork |
Ricci flow with surgery on three-manifolds
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The entropy formula for the Ricci flow and its geometric applications NERFINISHED ⓘ |
| resultType |
existence theorem
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extinction time estimate ⓘ |
| status | unpublished in traditional journal at time of release ⓘ |
| usesConcept |
Riemannian metrics
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curvature conditions ⓘ |
| usesMethod | Ricci flow with surgery ⓘ |
| year | 2003 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Grigori Perelman
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notableWork
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"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds"
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