Description
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.
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 Poincare series in one variable Quasiconformal mappings and Teichmuller'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 Teichmuller spaces An approximation theorem Automorphic forms and Poincare series for infinitely generated Fuchsian groups Automorphic forms and general Teichmuller spaces A non-standard integral equation with applications to quasiconformal mappings On Ahlfors' finiteness theorem Inequalities for finitely generated Kleinian groups Universal Teichmuller space On boundaries of Teichmuller spaces and on Kleinian groups. I $L_1$ approximation of analytic functions Spaces of Kleinian groups Acknowledgments Part 2: Extremal quasiconformal mappings Isomorphisms between Teichmuller spaces Eichler integrals with singularities Uniformization, moduli, and Kleinian groups A remark on Mumford's compactness theorem Fiber spaces over Teichmuller spaces Poincare 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 Teichmuller spaces and generalizations On trace formula On iterates of hyperbolic transformations of Teichmuller space On a theorem of Abikoff An inequality for Riemann surfaces Holomorphic families of isomorphisms of Mobius groups Fricke spaces Holomorphic families of injections On Teichmuller's proof of Teichmuller's theorem On Sullivan's proof of the finiteness theorem and the eventual periodicity theorem The migration of European mathematicians to America Acknowledgments.
by "Nielsen BookData"