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Selected Works of Lipman Bers: Papers on Complex Analysis
Edited by: Irwin Kra and Bernard Maskit, State University of New York at Stony Brook, NY
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Collected Works
1998; 1134 pp; hardcover
Volume: 9
ISBN-10: 0-8218-0858-3
ISBN-13: 978-0-8218-0858-0
List Price: US$273
Member Price: US$218.40
Order Code: CWORKS/9
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See also:

Lipa's Legacy - Jozef Dodziuk and Linda Keen

In the Tradition of Ahlfors and Bers: Proceedings of the First Ahlfors-Bers Colloquium - Irwin Kra and Bernard Maskit

One of the founders of a major modern branch of complex analysis, Lipman Bers made fundamental contributions to the modern theory of Kleinian groups and moduli of Riemann surfaces. This volume is a collection of Bers' papers in complex analysis. Included are seminal papers in the field and articles by the editors and other colleagues discussing Bers' achievements and influence on the mathematical developments of the second half of the 20th century. Lists of his students, his publications, and reprints of hard-to-find papers are included.

Readership

Graduate students, research mathematicians and physicists working in complex analysis.

Reviews

"In bringing out this fine two-volume set, the editors have made a valuable contribution to the further development of complex analysis."

-- Mathematical Reviews

"The two volumes document the historical development and progress in research on the subjects made by one of its outstanding figures during almost half a century, with intimate connections to the work of others, including Ahlfors, I.N. Vekua, and the many students of Bers."

-- Zentralblatt MATH

Table of Contents

Part 1. Research Papers
  • On bounded analytic functions of two complex variables in certain domains with distinguished boundary surface
  • On rings of analytic functions
  • Singularities of minimal surfaces
  • Isolated singularities of minimal surfaces
  • Abelian minimal surfaces
  • Boundary value problems for minimal surfaces with singularities at infinity
  • Univalent solutions of linear elliptic systems
  • On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications
  • On linear and non-linear elliptic boundary values in the plane
  • Local behavior of solutions of general linear elliptic equations
  • An outline of the theory of pseudoanalytic functions
  • Formal powers and power series
  • On a theorem of Mori and the definition of quasiconformality
  • Simultaneous uniformization
  • Spaces of Riemann surfaces as bounded domains
  • Riemann's mapping theorem for variable metrics
  • Uniformization and moduli
  • Completeness theorems for Poincaré series in one variable
  • Quasiconformal mappings and Teichmüller's theorem
  • Spaces of Riemann surfaces
  • Holomorphic differentials as functions of moduli
  • Uniformization by Beltrami equations
  • The equivalence of two definitions of quasiconformal mappings
  • Holomorphic convexity of Teichmüller spaces
  • An approximation theorem
  • Automorphic forms and Poincaré series for infinitely generated Fuchsian groups
  • Automorphic forms and general Teichmüller spaces
  • A non-standard integral equation with applications to quasiconformal mappings
  • On Ahlfors' finiteness theorem
  • Inequalities for finitely generated Kleinian groups
  • Universal Teichmüller space
  • On boundaries of Teichmüller spaces and on Kleinian groups. I
  • \(L_1\) approximation of analytic functions
  • Spaces of Kleinian groups
  • Acknowledgments
Part 2
  • Extremal quasiconformal mappings
  • Isomorphisms between Teichmüller spaces
  • Eichler integrals with singularities
  • Uniformization, moduli, and Kleinian groups
  • A remark on Mumford's compactness theorem
  • Fiber spaces over Teichmüller spaces
  • Poincaré series for Kleinian groups
  • Spaces of degenerating Riemann surfaces
  • On spaces of Riemann surfaces with nodes
  • Automorphic forms for Schottky groups
  • Deformations and moduli of Riemann surfaces with nodes and signatures
  • On Hilbert's 22nd problem
  • Nielsen extensions of Riemann surfaces
  • The action of the universal modular group on certain boundary points
  • Quasiconformal mappings, with applications to differential equations, function theory, and topology
  • An extremal problem for quasiconformal mappings and a theorem by Thurston
  • An application of quasiconformal mappings to topology
  • A new proof of a fundamental inequality for quasiconformal mappings
  • The action of the modular group on the complex boundary
  • Finite dimensional Teichmüller spaces and generalizations
  • On trace formula
  • On iterates of hyperbolic transformations of Teichmüller space
  • On a theorem of Abikoff
  • An inequality for Riemann surfaces
  • Holomorphic families of isomorphisms of Möbius groups
  • Fricke spaces
  • Holomorphic families of injections
  • On Teichmüller's proof of Teichmüller's theorem
  • On Sullivan's proof of the finiteness theorem and the eventual periodicity theorem
  • The migration of European mathematicians to America
  • Acknowledgments
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