Abreu equation
E1017919
equation in Kähler geometry
equation in toric geometry
fourth-order differential equation
nonlinear differential equation
partial differential equation
The Abreu equation is a fourth-order nonlinear partial differential equation arising in Kähler and toric geometry, particularly in the study of extremal and constant scalar curvature Kähler metrics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Abreu equation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13035698 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Abreu equation Context triple: [Monge–Ampère equation, relatedTo, Abreu equation]
-
A.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
-
B.
Charney equation
The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.
-
C.
Carothers equation
The Carothers equation is a fundamental relation in polymer chemistry that links the average degree of polymerization to the extent of reaction in step-growth polymerizations.
-
D.
Karplus equation
The Karplus equation is an empirical relationship in nuclear magnetic resonance (NMR) spectroscopy that correlates three-bond scalar coupling constants with dihedral angles, enabling the determination of molecular conformations.
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E.
Goodman–Martínez–Thompson correlation
The Goodman–Martínez–Thompson correlation is the most widely accepted scholarly conversion formula that aligns dates in the ancient Maya Long Count calendar with the Gregorian calendar.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Abreu equation Target entity description: The Abreu equation is a fourth-order nonlinear partial differential equation arising in Kähler and toric geometry, particularly in the study of extremal and constant scalar curvature Kähler metrics.
-
A.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
-
B.
Charney equation
The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.
-
C.
Carothers equation
The Carothers equation is a fundamental relation in polymer chemistry that links the average degree of polymerization to the extent of reaction in step-growth polymerizations.
-
D.
Karplus equation
The Karplus equation is an empirical relationship in nuclear magnetic resonance (NMR) spectroscopy that correlates three-bond scalar coupling constants with dihedral angles, enabling the determination of molecular conformations.
-
E.
Goodman–Martínez–Thompson correlation
The Goodman–Martínez–Thompson correlation is the most widely accepted scholarly conversion formula that aligns dates in the ancient Maya Long Count calendar with the Gregorian calendar.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
equation in Kähler geometry
ⓘ
equation in toric geometry ⓘ fourth-order differential equation ⓘ nonlinear differential equation ⓘ partial differential equation ⓘ |
| appearsIn |
constant scalar curvature Kähler (cscK) problem
ⓘ
theory of extremal metrics on toric manifolds ⓘ |
| appliesTo |
Delzant toric varieties
ⓘ
linked to:
Symplectic Toric Manifolds
compact toric Kähler manifolds ⓘ |
| arisesIn |
Kähler geometry
ⓘ
toric geometry ⓘ |
| associatedWith |
Delzant polytopes
ⓘ
linked to:
Convex Polytopes
toric symplectic manifolds ⓘ |
| characterizes |
toric constant scalar curvature Kähler metrics
ⓘ
toric extremal Kähler metrics ⓘ |
| definedOn | moment polytope of a toric Kähler manifold ⓘ |
| domain | convex functions on a Delzant polytope ⓘ |
| field | mathematics ⓘ |
| governs | scalar curvature in symplectic coordinates on toric manifolds ⓘ |
| hasDifferentialOrder | four ⓘ |
| hasOrder | 4 ⓘ |
| introducedBy | Miguel Abreu ⓘ |
| involves |
Hessian of a convex function
ⓘ
inverse Hessian matrix ⓘ symplectic potential ⓘ |
| isGeometricPDE | true ⓘ |
| isNonlinear | true ⓘ |
| namedAfter | Miguel Abreu ⓘ |
| relatedTo |
Calabi functional minimization
ⓘ
Monge–Ampère equation ⓘ extremal vector fields ⓘ |
| relatesTo | scalar curvature of a toric Kähler metric ⓘ |
| requires | boundary conditions on the moment polytope ⓘ |
| studiedIn |
complex differential geometry
ⓘ
geometric analysis ⓘ |
| subfield |
PDE theory
ⓘ
complex geometry ⓘ differential geometry ⓘ symplectic geometry ⓘ |
| usedFor |
study of constant scalar curvature Kähler metrics
ⓘ
study of extremal Kähler metrics ⓘ |
| yearIntroduced | 1998 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Abreu equation Description of subject: The Abreu equation is a fourth-order nonlinear partial differential equation arising in Kähler and toric geometry, particularly in the study of extremal and constant scalar curvature Kähler metrics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.