Edited by
Reiner Kuhnau, Martin Luther Universität, Halle-Wittenberg, Germany
Description
Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings.
Beginning
with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side
there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates,
so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical
Scharz lemma, and then Koebe's distortion theorem.
There are several connections to mathematical physics, because of the relations
to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and
further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane).
Audience:
Institutes of mathematics (and computer sciences). Institutes of physics and engineering.
