Geodesic
On the Radius of Curvature for Convex Analytic Functions
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 486-491

Voir la notice de l'article provenant de la source Cambridge University Press

Definition 1.1. Let be analytic for |z| < 1. If ƒ is univalent, we say that ƒ belongs to the class S. Definition 1.2. Let ƒ ∈ S, 0 ≦ α < 1. Then ƒ belongs to the class of convex functions of order α, denoted by Kα, provided (1) and if > 0 is given, there exists Z0, |Z0| < 1, such that Let ƒ ∈ Kα and consider the Jordan curve Υτ = ƒ(|z| = r), 0 < r < 1. Let s(r, θ) measure the arc length along Υτ; and let φ(r, θ) measure the angle (in the anti-clockwise sense) that the tangent line to Υτ at ƒ(reiθ) makes with the positive real axis. 
Eenigenburg, Paul. On the Radius of Curvature for Convex Analytic Functions. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 486-491. doi: 10.4153/CJM-1970-056-5
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