Open access peer-reviewed Edited Volume

Conformal Maps

Miodrag Mateljević

University of Belgrade


The Schwarz-Pick Theorem The Poincare Metric Conformal Invariants Geometric Function Theory Riemann Mapping Theorem Conformal GeometryPotential Theory Schwarz-Christoffel Integrals Harmonic Functions Dirichlet Problem Quasiconformal Mapping Holomorphic Motions Arbitrary Riemann Surfaces

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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.

Publishing process

Book initiated and editor appointed

Date completed: October 29th 2019

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline Extended: Open for Submissions

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

Approved chapters written in full and submitted

Deadline for full chapters: January 18th 2020

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: April 7th 2020

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: June 6th 2020

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About the editor

Miodrag Mateljević

University of Belgrade

Dr. Matljevic was Dean of the Faculty of Mathematics, University of Belgrade 2007-2014, corresponding member of the Serbian Academy of Sciences & Arts from 2012-2018, academician of the Serbian Academy of Sciences & Arts from November 8, 2018. He spent the winter semester 1988 as an associate professor at the University of Pittsburgh, and Associate Professorship during 1988/89. at Wayne State University, Detroit. His research is related to harmonic mappings, quasiconformal mapping, geometric inequalities, and elliptic partial differential equations. He published about 100 scientific papers in well internationally known journals. Dr. Matljevic delivered about 30 invited lectures and about 10 plenary lectures.

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