Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-30
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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Univalent holomorphic functions
Definition
Let be a complex domain. A holomorphic function is univalent when it is injective.
Thus "univalent" on a plane domain means exactly "one-to-one and holomorphic" on that domain.
Used by
- A quarter-disc inclusion at every point of a univalent disc map Corollary
- Bloch radii and the Bloch constant Definition
- The extremal family of disc-valued univalent maps fixing a basepoint Definition
- The normalized univalent class on the unit disc Definition
- A nonconstant locally uniform limit of univalent functions is univalent Lemma
- Controlled derivative oscillation forces injectivity on a fixed subdisc Lemma
- The area theorem for exterior univalent functions Theorem
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Matthias Weber, Complex Analysis, §7.5 (standard reference, not scraped)
- Walter Rudin, Real and Complex Analysis, Ch. 14 (standard reference, not scraped)