positive mass theorem
E603722
The positive mass theorem is a fundamental result in differential geometry and general relativity stating that, under suitable conditions, the total mass of an isolated gravitational system is nonnegative and vanishes only for flat spacetime.
All labels observed (2)
| Label | Occurrences |
|---|---|
| positive mass theorem canonical | 1 |
| positive mass theorem in general relativity | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6514674 — 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: positive mass theorem Context triple: [Richard Schoen, notableWork, positive mass theorem]
-
A.
Perelman’s entropy functionals
Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
-
B.
Poincaré conjecture
The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
-
C.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
-
D.
geometrization conjecture
The geometrization conjecture is a fundamental statement in 3-dimensional topology that classifies all closed 3-manifolds into pieces each admitting one of eight canonical geometric structures, a result proven by Grigori Perelman.
-
E.
Nirenberg problem in differential geometry
The Nirenberg problem in differential geometry is a classical question about prescribing Gaussian curvature on the 2-sphere via conformal deformations of the metric.
- 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: positive mass theorem Target entity description: The positive mass theorem is a fundamental result in differential geometry and general relativity stating that, under suitable conditions, the total mass of an isolated gravitational system is nonnegative and vanishes only for flat spacetime.
-
A.
Perelman’s entropy functionals
Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
-
B.
Poincaré conjecture
The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
-
C.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
-
D.
geometrization conjecture
The geometrization conjecture is a fundamental statement in 3-dimensional topology that classifies all closed 3-manifolds into pieces each admitting one of eight canonical geometric structures, a result proven by Grigori Perelman.
-
E.
Nirenberg problem in differential geometry
The Nirenberg problem in differential geometry is a classical question about prescribing Gaussian curvature on the 2-sphere via conformal deformations of the metric.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in differential geometry ⓘ result in general relativity ⓘ |
| alsoKnownAs | positive energy theorem NERFINISHED ⓘ |
| alternativeProofMethod | spinor methods ⓘ |
| appliesTo |
initial data sets for Einstein field equations
ⓘ
time-symmetric initial data in the Riemannian case ⓘ |
| asserts |
total mass is nonnegative under suitable conditions
ⓘ
total mass vanishes only for flat spacetime ⓘ |
| assumes |
asymptotically flat spacetime
ⓘ
dominant energy condition ⓘ |
| concerns |
ADM mass
ⓘ
Bondi mass NERFINISHED ⓘ total mass of an isolated gravitational system ⓘ |
| ensures | ADM mass is nonnegative for suitable asymptotically flat manifolds NERFINISHED ⓘ |
| field |
differential geometry
ⓘ
general relativity NERFINISHED ⓘ mathematical relativity ⓘ |
| firstCompleteProofYear | 1979 ⓘ |
| generalizedBy |
positive mass theorem in higher dimensions
ⓘ
positive mass theorem with charge NERFINISHED ⓘ |
| hasVersion |
Lorentzian positive mass theorem
NERFINISHED
ⓘ
Riemannian positive mass theorem NERFINISHED ⓘ minimal surface proof version ⓘ spinorial proof version ⓘ |
| implies |
Minkowski spacetime is the unique zero-mass solution under the hypotheses
NERFINISHED
ⓘ
no negative-mass isolated gravitational systems under the hypotheses ⓘ stability of Minkowski spacetime with respect to mass ⓘ |
| influenced |
geometric analysis
ⓘ
global differential geometry ⓘ mathematical foundations of general relativity ⓘ |
| originalProofMethod | minimal surface techniques ⓘ |
| provedBy |
Edward Witten
NERFINISHED
ⓘ
Richard Schoen NERFINISHED ⓘ Shing-Tung Yau NERFINISHED ⓘ |
| relatedTo |
Penrose inequality
NERFINISHED
ⓘ
Yamabe problem NERFINISHED ⓘ cosmic censorship conjecture NERFINISHED ⓘ |
| requiresCondition |
appropriate decay of the metric at infinity
ⓘ
nonnegative scalar curvature in the Riemannian version ⓘ |
| spinorialProofYear | 1981 ⓘ |
| usesConcept |
ADM 4-momentum
NERFINISHED
ⓘ
asymptotically flat Riemannian manifold ⓘ energy conditions ⓘ scalar curvature ⓘ |
| zeroMassCase |
manifold is isometric to Euclidean space in the Riemannian version
ⓘ
spacetime is isometric to Minkowski spacetime in the Lorentzian version ⓘ |
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: positive mass theorem Description of subject: The positive mass theorem is a fundamental result in differential geometry and general relativity stating that, under suitable conditions, the total mass of an isolated gravitational system is nonnegative and vanishes only for flat spacetime.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
positive mass theorem in general relativity