Three-manifolds with positive Ricci curvature
E888034
"Three-manifolds with positive Ricci curvature" is a landmark 1982 paper by Richard S. Hamilton that introduced the Ricci flow and launched the modern geometric analysis approach to understanding the topology of three-dimensional manifolds.
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
landmark paper in geometric analysis
ⓘ
mathematics research paper ⓘ |
| assumes | positive lower bound on Ricci curvature ⓘ |
| author | Richard S. Hamilton NERFINISHED ⓘ |
| citedFor |
classification results for positively Ricci curved 3-manifolds
ⓘ
introduction and analysis of Ricci flow on 3-manifolds ⓘ |
| contribution |
applied Ricci flow to study topology of 3-manifolds
ⓘ
launched modern geometric analysis approach to 3-manifold topology ⓘ |
| establishes | long-time behavior of Ricci flow in dimension three under curvature conditions ⓘ |
| field |
Riemannian geometry
NERFINISHED
ⓘ
differential geometry ⓘ geometric analysis ⓘ |
| focusesOn | closed three-manifolds with positive Ricci curvature ⓘ |
| hasAuthorInitials | R. S. Hamilton NERFINISHED ⓘ |
| hasCurvatureCondition | positive Ricci curvature ⓘ |
| hasDimensionFocus | 3 ⓘ |
| historicalSignificance | first systematic use of Ricci flow in Riemannian geometry ⓘ |
| influenced |
Perelman’s work on the Poincaré conjecture
ⓘ
development of Ricci flow with surgery ⓘ |
| influencedField |
3-manifold topology
ⓘ
geometric evolution equations ⓘ global Riemannian geometry ⓘ |
| introducesConcept | Ricci flow NERFINISHED ⓘ |
| isConsidered |
foundational work in Ricci flow theory
ⓘ
starting point of modern program to classify 3-manifolds via geometric flows ⓘ |
| language | English ⓘ |
| mainTopic |
Ricci flow
NERFINISHED
ⓘ
positive Ricci curvature ⓘ three-dimensional manifolds ⓘ |
| mathematicalSubject |
curvature conditions on manifolds
ⓘ
topology of 3-manifolds ⓘ |
| publicationYear | 1982 ⓘ |
| relatedToConcept |
curvature pinching
ⓘ
normalized Ricci flow NERFINISHED ⓘ spherical space forms ⓘ |
| relatedToConjecture | Poincaré conjecture NERFINISHED ⓘ |
| result | proved that certain 3-manifolds with positive Ricci curvature are diffeomorphic to spherical space forms ⓘ |
| studies | behavior of curvature under Ricci flow ⓘ |
| studiesObject | Riemannian 3-manifolds ⓘ |
| usesMethod |
evolution equation for Riemannian metrics
ⓘ
maximum principle techniques ⓘ parabolic partial differential equations ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.