Geometric function theory

Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem.Schwarz Lemma. Let D = {z : |z| < 1} be the open unit disk in the complex plane C centered at the origin and let f : D → D be a holomorphic map such that f(0) = 0. Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem. The following are some of the most important topics in geometric function theory: A conformal map is a function which preserves angles locally. In the most common case the function has a domain and range in the complex plane.