Read more
Zusatztext 'The presentation of the whole theory is very nice...the book reads well! and will be interesting and accessible for mathematicians from several branches of mathematics' EMS Klappentext A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Mobius 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 produced important work which helped make Kleinian groups an active area of complex analysis as a branch of Teichmuller theory. Later, Thurston brought about a revolution in the field with his profound investigation of hyperbolic manifolds, and Sullivan developed an important complex dynamical approach. This book provides the fundamental results and key theorems necessary for access to the frontiers of the theory from a modern viewpoint. Zusammenfassung 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. Inhaltsverzeichnis 0: Hyperbolic surfaces and Fuchsian groups: summary 1: Hyperbolic 3-manifolds 2: The basis of Kleinian group theory 3: Geometrically finite Kleinian groups 4: Finitely generated Kleinian groups 5: The sphere at infinity 6: Infinite ends of hyperbolic manifolds 7: Algebraic and geometric convergences Appendix References ...
