A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of M�bius 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 Teichm�ller 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.
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Editorial Reviews
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"The subject of this monograph is the modern theory of Kleinian groups as developed by Ahlfors, Bers, Thurston and their students. It prepares the reader for the current work on the subject."--Mathematical Reviews
Language Notes
Text: English (translation)
Original Language: Japanese
Original Language: Japanese
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2 of 3 people found the following review helpful:
4.0 out of 5 stars
Good Introduction to the zoo of Hyperbolic Geometry,
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This review is from: Hyperbolic Manifolds and Kleinian Groups (Oxford Mathematical Monographs) (Hardcover)
This book is intended to introduce readers to Hyperbolic Geometry in 3 dimensions. The book covers from a review of hyperbolic surfaces to the classification program of 3-manifold initiated by Thurston.
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