Books written by Lars Ahlfors.
Ahlfors was awarded the Fields Medal in 1938 for research on covering surfaces related to Riemann surfaces of inverse functions of entire and meromorphic functions. Opened up new fields of analysis.
A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material.
Conformal Invariants: Topics in Geometric Function Theory
The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never appeared in book form, particularly the discussion of the theory of extremal length.
The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions.
Advances in the Theory of Riemann Surfaces
The present volume contains all but two of the papers read at the conference, as well as a few papers and short notes submitted afterwards. We hope that it reflects faithfully the present state of research in the fields covered, and that it may provide an access to these fields for future investigations.
Contributions to the Theory of Riemann Surfaces
Volume 30 (Annals of Mathematics Studies)
Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers
Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers is a compendium of papers provided by Bers, friends, students, colleagues, and professors. These papers deal with Teichmuller spaces, Kleinian groups, theta functions, algebraic geometry. Other papers discuss quasiconformal mappings, function theory, differential equations, and differential topology.
A survey of recent (1960) developments both in the classical and modern fields of the theory. Contents include: The complex analytic structure of the space of closed Riemann surfaces; Complex analysis on noncompact Riemann domains; Proof of the Teichmuller-Ahlfors theorem; The conformal mapping of Riemann surfaces; On certain coefficients of univalent functions
Lectures on Quasiconformal Mappings
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