Statements (12)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:unit_disk
holomorphic functions |
| gptkbp:field |
complex analysis
|
| gptkbp:generalizes |
gptkb:Schwarz–Pick_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Obey Schwarz Lemma
|
| gptkbp:implies |
maximum modulus principle
rigidity of holomorphic maps |
| gptkbp:namedAfter |
gptkb:Hermann_Amandus_Schwarz
|
| 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:bfsParent |
gptkb:Analytic_Functions
|
| gptkbp:bfsLayer |
6
|