Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:unit_disk
holomorphic functions |
| gptkbp:category |
theorems in complex analysis
|
| gptkbp:countryOfOrigin |
gptkb:Germany
|
| gptkbp:field |
complex analysis
|
| gptkbp:firstPublished |
1869
|
| gptkbp:generalizes |
gptkb:Schwarz–Pick_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schwarz lemma
|
| gptkbp:implies |
maximum modulus principle
rigidity of holomorphic maps |
| gptkbp:namedAfter |
gptkb:Hermann_Amandus_Schwarz
|
| gptkbp:relatedTo |
automorphisms of the unit disk
conformal maps |
| gptkbp:sentence |
If a holomorphic function f from the unit disk to itself fixes the origin, then |f(z)| ≤ |z| for all z in the disk and |f'(0)| ≤ 1.
|
| gptkbp:usedIn |
proof of Riemann mapping theorem
|
| gptkbp:bfsParent |
gptkb:Hermann_Amandus_Schwarz
gptkb:Hermann_Schwarz gptkb:Komplexe_Analysis |
| gptkbp:bfsLayer |
6
|