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The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a mini-conference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program.
List of contents
Table of Contents - Volume L.- Complex Dynamics.- The Nonconjugacy of Certain Exponential Functions.- Dynamics of Holomorphic Self-Maps OF ?*.- Automorphisms of Rational Maps.- Geometric Function Theory.- Selfsimilar Zippers.- On the Boundary Behavior of Bloch Functions.- Harmonic Functions in Quasicircle Domains.- Note on A Theorem of Wolff.- Bloch and Normal Functions on General Planar Regions.- A Halfplane Version of A Theorem of Borel.- An Index Theorem on Singular Points and Cusps of Quadrature Domains.- The Local Modulus of Continuity of an Analytic Function.- Quasiconformal Mappings.- Quasiconformal Isotopies.- The Coefficient Problem for Univalent Functions with Quasiconformal Extension.- Cone Conditions and Quasiconformal Mappings.- Existence of Quasiregular Mappings.- Quasisymmetric Maps.- A Geometric Interpretation of the Ahlfors-Weill Mappings and an Induced Foliation of ?3.- Riemann Surfaces.- Isospectral Potentials on A Surface of Genus 3.- Integrable Holomorphic Quadratic Differentials With Simple Zeros.- Lower Bounds for the Number of Saddle Connections and Closed Trajectories of A Quadratic Differential.- Rational Solutions of and Simple Closed Geodesics on Fricke Surfaces.- The Period Matrices of Compact Continuations of an Open Rlemann Surface of Finite Genus.
