Quasiconformal Mappings In The Plane And Complex Dynamics
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Quasiconformal Mappings in the Plane and Complex Dynamics
This book comprehensively explores the foundations of quasiconformal mappings in the complex plane, especially in view of applications to complex dynamics. Besides playing a crucial role in dynamical systems these mappings have important applications in complex analysis, geometry, topology, potential theory and partial differential equations, functional analysis and calculus of variations, electrostatics and nonlinear elasticity . The work covers standard material suitable for a one-year graduate-level course and extends to more advanced topics, in an accessible way even for students in an initial phase of university studies who have learned the basics of complex analysis at the usual level of a rigorous first one-semester course on the subject. At the frontier of complex analysis with real analysis, quasiconformal mappings appeared in 1859-60 in the cartography work of A. Tissot, well before the term “quasiconformal” was coined by L. Ahlfors in 1935. The detailed study of these mappings began in 1928 by H. Grötzsch, and L. Ahlfors’ seminal work published in 1935 significantly contributed to their development and was considered for awarding him the Fields Medal in 1936. The theory further evolved in 1937 and 1939 with O. Teichmüller’s contributions, and subsequent advancements are partially covered in this book. Organized into ten chapters with eight appendices, this work aims to provide an accessible, self-contained approach to the subject and includes examples at various levels and extensive applications to holomorphic dynamics. Throughout the text, historical notes contextualize advancements over time. A sequel to the author’s previous book, ‘Complex Analysis and Dynamics in One Variable with Applications,’ also published by Springer, this volume might be suitable for students in mathematics, physics, or engineering. A solid background in basic mathematical analysis is recommended to fully benefit from its content.
Quasiconformal Mappings and Analysis
Author: Peter Duren
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on ""Quasiconformal mappings and analysis"" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.
Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces
Author: Yunping Jiang
language: en
Publisher: American Mathematical Soc.
Release Date: 2012
This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.