DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-30

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The normalized univalent class on the unit disc

Definition

The normalized univalent class is

$S : = {f : D \to C : f is holomorphic and univalent, f (0) = 0, f^{'} (0) = 1},$

where univalence is that of Univalent holomorphic functions.

Depends on

Univalent holomorphic functions

Used by

The second coefficient of a normalized univalent function has modulus at most two Corollary
Every normalized univalent disc map contains the quarter disc Theorem
Koebe's distortion theorem Theorem
Koebe's growth theorem Theorem

Dependency tree · one level

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Sources

Matthias Weber, Complex Analysis, §7.5 (standard reference, not scraped)
Walter Rudin, Real and Complex Analysis, Ch. 14 (standard reference, not scraped)