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.
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.
More formally, a map,
is called conformal (or angle-preserving) at a point if it preserves oriented angles between curves through with respect to their orientation (i.e., not just the magnitude of the angle). Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature.
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