Two-Sided Estimate of Univalence Domains for Holomorphic Mappings of the Unit Disk into Itself Keeping Its Diameter

摘要

We obtain an asymptotically sharp two-sided estimate of univalence domains on classes of holomorphic automorphisms of the unit disc with two boundary fixed points and an invariant diameter. The estimate depends on the value of the product of the angular derivatives at the boundary fixed points.