Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:concept
|
| gptkbp:bfsLayer |
6
|
| gptkbp:bfsParent |
gptkb:Richard_Perelman
|
| gptkbp:analyzes |
a heat equation for metrics
|
| gptkbp:application |
deforming the metric
numerically simulated |
| gptkbp:applies_to |
Riemannian manifolds
complex manifolds |
| gptkbp:can_be_extended_by |
higher dimensions
Kähler metrics |
| gptkbp:can_lead_to |
singularities
|
| gptkbp:developed_by |
gptkb:Richard_S._Hamilton
|
| gptkbp:displacement |
the metric tensor
|
| gptkbp:exhibits |
convergence properties
|
| gptkbp:flows_into |
Riemannian metrics
analyzed using PDE techniques applied in mathematical physics contexts applied to various geometric problems the geometry of a manifold used to analyze geometric structures. used to study geometric evolution equations used to study the topology of manifolds |
| gptkbp:formed |
singularities in finite time
|
| gptkbp:has_expansion |
other geometric flows
|
| gptkbp:has_programs |
gptkb:physicist
|
| https://www.w3.org/2000/01/rdf-schema#label |
Ricci Flow
|
| gptkbp:is_a_solution_for |
the Ricci equation
|
| gptkbp:is_a_tool_for |
understanding the geometry of manifolds
understanding curvature dynamics |
| gptkbp:is_analyzed_in |
the maximum principle
|
| gptkbp:is_connected_to |
gptkb:television_channel
|
| gptkbp:is_essential_for |
the classification of manifolds
|
| gptkbp:is_influenced_by |
the initial metric
|
| gptkbp:is_related_to |
Einstein equations
the concept of curvature the concept of Ricci solitons |
| gptkbp:is_studied_in |
mathematical physics
Kähler-Ricci flow |
| gptkbp:is_tested_for |
the uniformization theorem
|
| gptkbp:is_used_in |
geometric analysis
the proof of the Poincaré conjecture |
| gptkbp:key |
the study of Ricci curvature
the study of 3-manifolds |
| gptkbp:related_concept |
historical significance in mathematics
|
| gptkbp:significance |
modern geometry
|
| gptkbp:subject |
differential geometry
active research |
| gptkbp:technique |
understanding geometric structures
smoothing metrics |
| gptkbp:type_of |
differential equation
|