Statements (70)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:concept
|
| gptkbp:bfsLayer |
4
|
| gptkbp:bfsParent |
gptkb:Poincaré_conjecture
|
| gptkbp:applies_to |
gptkb:musician
mathematical modeling Riemannian manifolds non-compact manifolds |
| gptkbp:can_lead_to |
formation of singularities
|
| gptkbp:challenges |
gptkb:University
computational complexity singularity analysis |
| gptkbp:collaborated_with |
research groups
|
| gptkbp:collaborations |
other mathematical fields
|
| gptkbp:developed_by |
gptkb:Richard_S._Hamilton
|
| gptkbp:examines |
gptkb:Mathematician
graduate studies |
| https://www.w3.org/2000/01/rdf-schema#label |
Ricci flow with surgery
|
| gptkbp:integrates_with |
modern mathematical research
|
| gptkbp:involves |
surgery techniques
|
| gptkbp:is_a |
method for evolving metrics
method in geometric analysis |
| gptkbp:is_analyzed_in |
research articles
topological methods |
| gptkbp:is_associated_with |
Ricci curvature
|
| gptkbp:is_challenged_by |
alternative theories
|
| gptkbp:is_characterized_by |
deformation of the metric
|
| gptkbp:is_connected_to |
differential equations
Einstein metrics |
| gptkbp:is_considered |
mathematical physics
|
| gptkbp:is_criticized_for |
mathematical reviews
|
| gptkbp:is_discussed_in |
gptkb:academic_conferences
online forums |
| gptkbp:is_documented_in |
gptkb:book
mathematical literature |
| gptkbp:is_enhanced_by |
new techniques
|
| gptkbp:is_essential_for |
3-manifold topology
|
| gptkbp:is_evaluated_by |
peer review
|
| gptkbp:is_explored_in |
case studies
numerical analysis theoretical mathematics mathematical seminars doctoral theses |
| gptkbp:is_fundamental_to |
understanding geometric structures
|
| gptkbp:is_implemented_in |
numerical simulations
|
| gptkbp:is_influenced_by |
historical developments in geometry
|
| gptkbp:is_influential_in |
modern geometry
|
| gptkbp:is_noted_for |
its complexity
|
| gptkbp:is_part_of |
geometric topology
|
| gptkbp:is_promoted_by |
gptkb:Educational_Institution
|
| gptkbp:is_recognized_by |
mathematical societies
|
| gptkbp:is_reflected_in |
research papers
|
| gptkbp:is_related_to |
gptkb:Perelman’s_proof_of_the_Poincaré_conjecture
|
| gptkbp:is_studied_in |
differential geometry
its applications in topology |
| gptkbp:is_supported_by |
grants
computational tools academic funding |
| gptkbp:is_used_to |
prove geometrization conjecture
|
| gptkbp:is_utilized_in |
theoretical physicists
research collaborations understanding curvature behavior |
| gptkbp:key |
solving geometric problems
|
| gptkbp:presented_by |
symposiums
|
| gptkbp:provides |
singularity formation analysis
|
| gptkbp:published_by |
mathematical journals
|
| gptkbp:related_to |
gptkb:Ricci_flow
|
| gptkbp:requires |
initial conditions
|
| gptkbp:specialization |
physics and engineering
|
| gptkbp:training |
advanced mathematics courses
|
| gptkbp:used_in |
geometric analysis
|