Every normalised univalent (injective and holomorphic) map f from the unit disk into ℂ has image containing the ball B(0, 1/4). Extremal: the Koebe function K(z) = z/(1−z)² attains equality, with K(−1) = −1/4. Proof uses area theorem…
Every normalised univalent (injective and holomorphic) map f from the unit disk into ℂ has image containing the ball B(0, 1/4). Extremal: the Koebe function K(z) = z/(1−z)² attains equality, with K(−1) = −1/4. Proof uses area theorem…