maximum modulus principle
E1463336
UNEXPLORED
The maximum modulus principle is a fundamental result in complex analysis stating that a non-constant holomorphic function on a connected open set cannot attain its maximum modulus in the interior, only on the boundary.
All labels observed (1)
| Label | Occurrences |
|---|---|
| maximum modulus principle canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T21047230 — 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: maximum modulus principle Context triple: [Lindelöf theorem in complex analysis, refines, maximum modulus principle]
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A.
Schwarz lemma
Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
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B.
Borel–Carathéodory theorem
The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
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C.
Schwarz–Pick theorem
The Schwarz–Pick theorem is a fundamental result in complex analysis that characterizes holomorphic self-maps of the unit disk by showing they are distance-decreasing with respect to the hyperbolic (Poincaré) metric.
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D.
Casorati–Weierstrass theorem
The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
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E.
Rouché's theorem
Rouché's theorem is a result in complex analysis that provides conditions under which two holomorphic functions have the same number of zeros inside a given contour.
- 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: maximum modulus principle Target entity description: The maximum modulus principle is a fundamental result in complex analysis stating that a non-constant holomorphic function on a connected open set cannot attain its maximum modulus in the interior, only on the boundary.
-
A.
Schwarz lemma
Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
-
B.
Borel–Carathéodory theorem
The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
-
C.
Schwarz–Pick theorem
The Schwarz–Pick theorem is a fundamental result in complex analysis that characterizes holomorphic self-maps of the unit disk by showing they are distance-decreasing with respect to the hyperbolic (Poincaré) metric.
-
D.
Casorati–Weierstrass theorem
The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
-
E.
Rouché's theorem
Rouché's theorem is a result in complex analysis that provides conditions under which two holomorphic functions have the same number of zeros inside a given contour.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.