Univalent function

Summary

A univalent function is a holomorphic function that is injective on its domain. It is a conformal map of its domain onto its image, which is again an open set. The theory of univalent functions studies the class $S$ of univalent functions on the unit disc with $f(0) = 0$ and $f'(0) = 1$. Its main results are distortion, covering and coefficient theorems, such as the Koebe quarter theorem and the Bieberbach conjecture.