| 書目名稱 | Kleinian Groups | | 編輯 | Bernard Maskit | | 視頻video | http://file.papertrans.cn/544/543371/543371.mp4 | | 叢書名稱 | Grundlehren der mathematischen Wissenschaften | | 圖書封面 |  | | 描述 | 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, a | | 出版日期 | Book 1988 | | 關(guān)鍵詞 | Area; Dimension; Finite; Group theory; Invariant; Riemann surface; approximation; convergence; field; finite | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-61590-0 | | isbn_softcover | 978-3-642-64878-6 | | isbn_ebook | 978-3-642-61590-0Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin Heidelberg 1988 |
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