The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers; specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the Beltrami equation has deep implications for the theory of Kleinian groups and their deformations. From the point of view of uniformizations of Riemann surfaces, Bers' observation has the consequence that the question of understanding the different uniformizations of a finite Riemann surface poses a purely topological problem; it is independent of the conformal structure on the surface. The last two chapters here give a topological description of the set of all (geometrically finite) uniformizations of finite Riemann surfaces. We carefully skirt Ahlfors' finiteness theorem. For groups which uniformize a finite Riemann surface; that is, groups with an invariant component, one can either start with the assumption that the group is finitely generated, and then use the finiteness theorem to conclude that the group represents only finitely many finite Riemann surfaces, or, as we do here, one can start with the assumption that, in the invariant component, the group represents a finite Riemann surface, and then, using essentially topological techniques, reach the same conclusion. More recently, Bill Thurston wrought a revolution in the field by showing that one could analyze Kleinian groups using 3-dimensional hyperbolic geome try, and there is now an active school of research using these methods.
"synopsis" may belong to another edition of this title.
Book Description Book Condition: Brand New. Brand New Original US Edition, Perfect Condition. Printed in English. Excellent Quality, Service and customer satisfaction guaranteed!. Bookseller Inventory # AIND-30537
Book Description Book Condition: New. New. US edition. Perfect condition. Customer satisfaction our priority. Bookseller Inventory # ABE-FEB-117503
Book Description Book Condition: Brand New. New. US edition. Customer Satisfaction guaranteed!!. Bookseller Inventory # SHUB117503
Book Description Book Condition: New. Brand New Original US Edition.We Ship to PO BOX Address also. EXPEDITED shipping option also available for faster delivery. Bookseller Inventory # AUSBNEW-30537
Book Description Book Condition: Brand New. New, US edition. Excellent Customer Service. Bookseller Inventory # ABEUSA-117503
Book Description Springer. Book Condition: New. pp. xiii + 326 , 67 Figures. Bookseller Inventory # 7553082
Book Description Springer, 2017. Hardcover. Book Condition: New. Never used! This item is printed on demand. Bookseller Inventory # P113540177469
Book Description Springer, 2004. Hardcover. Book Condition: New. book. Bookseller Inventory # M3540177469
Book Description Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 1987. HRD. Book Condition: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IP-9783540177463
Book Description Springer Berlin Heidelberg 1987-11-23, Berlin, 1987. hardback. Book Condition: New. Bookseller Inventory # 9783540177463