Lectures on Quasiconformal Mappings

by Lars V. Ahlfors

Series:University Lecture Series (38)

Description

Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how show more Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings. show less

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Indeholder "Acknowledgments", "Chapter I. Differentiable Quasiconformal Mappings", " Introduction", " A. The Problem and Definition of Grötzsch", " B. Solution of Grötzsch's Problem", " C. Composed Mappings", " D. Extremal Length", " E. A Symmetry Principle", " F. Dirichlet Integrals", "Chapter II. The General Definition", " A. The Geometric Approach", " B. The Analytic Approach", "Chapter III. Extremal Geometric Properties", " A. Three Extremal Problems", " B. Elliptic and Modular Functions", " C. Mori's Theorem", " D. Quadruplets", "Chapter IV. Boundary Correspondence", " A. The M-condition", " B. The Sufficiency of the M-condition", " C. Quasi-isometry", " D. Quasiconformal Reflection", " E. The Reverse Inequality", "Chapter V. The show more Mapping Theorem", " A. Two Integral Operators", " B. Solution of the Mapping Problem", " C. Dependence on Parameters", " D. The Calderón-Zygmund Inequality", "Chapter VI. Teichmüller Spaces", " A. Preliminaries", " B. Beltrami Differentials", " C. Delta is Open", " D. The Infinitesimal Approach".

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Jan 23, 2022Danish

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