Masahiko Taniguchi – författare

A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought a revolution to this area with his profound investigation of hyperbolic manifolds, and at the same time complex dynamical approach was strongly developed by Sullivan. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.

This introduction to the theory of Teichmuller spaces will not only be used by graduate students and researchers in complex analysis and algebraic geometry, but also by theoretical physicists working with string theory. Starting with some basic facts on Riemann surfaces the authors provide a compehensive treatment of the subject and cover some very recent research topics. They have attempted to make the book as self-contained as possible and have included heuristic arguments and numerous examples.