I. Kra – författare

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.

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.

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.

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.

The present volume is the culmination often years'' work separately and joint­ ly. The idea of writing this book began with a set of notes for a course given by one of the authors in 1970-1971 at the Hebrew University. The notes were refined serveral times and used as the basic content of courses given sub­ sequently by each of the authors at the State University of New York at Stony Brook and the Hebrew University. In this book we present the theory of Riemann surfaces and its many dif­ ferent facets. We begin from the most elementary aspects and try to bring the reader up to the frontier of present-day research. We treat both open and closed surfaces in this book, but our main emphasis is on the compact case. In fact, Chapters III, V, VI, and VII deal exclusively with compact surfaces. Chapters I and II are preparatory, and Chapter IV deals with uniformization. All works on Riemann surfaces go back to the fundamental results of Rie­ mann, Jacobi, Abel, Weierstrass, etc. Our book is no exception. In addition to our debt to these mathematicians of a previous era, the present work has been influenced by many contemporary mathematicians.