A new variant of the Schwarz lemma is also proved for the Carathèodory class of analytic functions having positive real part in 𝔻. Our results lead to several improved estimates for the hyperbolic ...

M. Papadimitrakis, On Convexity of Level Curves of Harmonic Functions in the Hyperbolic Plane, Proceedings of the American Mathematical Society, Vol. 114, No. 3 (Mar., 1992), pp. 695-698 ...