Mejia and Minda proved that if a hyperbolic simply connected region Ω is κ-convex, then ｜▽ log λ_Ω (z)｜ ≤ λ_Ω (z) √(1 - 2κ/λ_Ω(z)), z ∈ Ω. We show that this inequality actually characterizes κ-convex regions.
