About the book
The subject of conformal mappings is a major part of GFT (Geometric Function Theory). Riemann mapping theorem — for every simply connected domain of the extended complex plane there is a meromorphic function that maps such a domain conformally onto the unit disk, has a significant impact on GFT. Most conformal invariants can be described in terms of extremal properties.
Conformal invariants and extremal problems are therefore intimately linked and form together with the central theme of this book.
This book also welcomes topics such as introduction to Riemann surfaces, with an outline of a proof of the uniformization theorem which can be considered as a generalization of the Riemann mapping theorem. The book also welcomes potential theory and some possible applications in different scientific disciplines, such as fluid flows, heat transfer, various mathematical models and methods, including solutions of certain integral equations.
The scopes of the book include, but are not limited to, the following fields: Geometric Function Theory, Applications of Schwarz's lemma, Conformal Invariants, Complex Analysis, and Potential Theory, Solutions of Beltrami equation and Theory of Beltrami operators and Harmonic Maps Between Surfaces.