2006/07/14 by Lars V. Ahlfors · 1,827 citations
Mathematics · #Analytic and geometric function theory #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Boundary (topology) #Mathematics #Pure mathematics #Quasiconformal mapping #Differentiable function #Teichmüller space #Mathematical analysis #Riemann surface
paper · doi:10.1090/ulect/038
published in University lecture series (American Mathematical Society)
openalex publication_date 2006/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/21
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 Teichm�ller spaces, including the Bers embedding and the Teichm�ller 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 Teichm�ller 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 Teichm�ller spaces and provides many references to the vast literature on Teichm�ller 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.