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.

Inhalt

Fuchsian Groups.- Mostow Rigidity on the Line: A Survey.- Fuchsian Groups and nth Roots of Parabolic Generators.- On the Existence of Elliptics in Subgroups of PSL(2, ?): a Graphical Picture.- The Kernel of the Poincaré Series Operator of Weight - 2.- Kleinian Groups and Generalizations.- Strange actions of Groups on Spheres, II.- Quasiconformal Groups and the Conical Limit Set.- Generic Fundamental Polyhedra for Kleinian Groups.- Quasiconformal Actions on Domains in Space.- Convergence and Möbius Groups.- The Limit Set of a Discrete Group of Hyperbolic Motions.- A Remark on a Paper by Floyd.- Purely Elliptic Möbius Groups.- Teichmüller Spaces.- Conformally Natural Reflections in Jordan Curves with Applications to Teichmüller Spaces.- A Theorem of Bers and Greenberg for Infinite Dimensional Teichmüller Spaces.- A Finiteness Theorem for Holomorphic Families of Riemann Surfaces.- Non-Variational Global Coordinates for Teichmüller Spaces.- Parameters for Fuchsian Groups I: Signature (0, 4).- Parametrization of Teichmüller Spaces by Geodesic Length Functions.- Families of Compact Riemann Surfaces Which do not Admit nth Roots.