Lectures on Quasiconformal Mappings (University Lecture Series) (University Lecture Series, 38)

Lars Ahlfors' 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 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. Readership: Graduate students and research mathematicians interested in complex analysis. 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 Teichmüller Spaces, Including The Bers Embedding And The Teichmüller Curve. It Is Remarkable How 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 Teichmüller 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 Teichmüller Spaces And Provides Many References To The Vast Literature On Teichmüller 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. Ch. I. Differentiable Quasiconformal Mappings -- Ch. Ii. The General Definition -- Ch. Iii. Extremal Geometric Properties -- Ch. Iv. Boundary Correspondence -- Ch. V. The Mapping Theorem -- Ch. Vi. Teichmuller Spaces -- A Supplement To Ahlfors's Lectures / Clifford J. Earle And Irwin Kra -- Complex Dynamics And Quasiconformal Mappings / Mitsuhiro Shishikura -- Hyperbolic Structures On Three-manifolds That Fiber Over The Circle / John H. Hubbard. Lars V. Ahlfors ; With Additional Chapters By C.j. Earle ... [et Al.]. Originally Published: Toronto ; New York : D. Van Nostrand Co., C1966. Includes Bibliographical References. Cover 1 Title page 4 Contents 6 Preface 8 Part I. The Ahlfors Lectures 10 Acknowledgments 12 Differentiable quasiconformal mappings 14 The general definition 24 Extremal geometric properties 32 Boundary correspondence 48 The mapping theorem 60 Teichmüller spaces 76 Editors’ notes 92 Part II. The Additional Chapters 94 A supplement to Ahlfors’s lectures 96 Complex dynamics and quasiconformal mappings 128 Hyperbolic structures on three-manifolds that fiber over the circle 152 Back Cover 178