On conformal mapping of a circle onto convex domains - Gutlyansky , V. Ya.; Kopanev, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
A series of sharp inequalities for conformal mappings of the disk onto convex domains is given, which connect the curvature, deviation, Schwarzian, and other characteristics of level lines and orthogonal trajectories.