书目名称 | Complex Kleinian Groups | 编辑 | Angel Cano,Juan Pablo Navarrete,José Seade | 视频video | http://file.papertrans.cn/232/231460/231460.mp4 | 概述 | Lays down the foundations of a new field of mathematics including areas as important as real and complex hyperbolic geometry, discrete group actions in complex geometry and the uniformization problem. | 丛书名称 | Progress in Mathematics | 图书封面 |  | 描述 | This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP.1.. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds. | 出版日期 | Book 2013 | 关键词 | Kleinian groups; complex hyperbolic geometry; discontinuity region; equicontinuity; limit set | 版次 | 1 | doi | https://doi.org/10.1007/978-3-0348-0481-3 | isbn_softcover | 978-3-0348-0805-7 | isbn_ebook | 978-3-0348-0481-3Series ISSN 0743-1643 Series E-ISSN 2296-505X | issn_series | 0743-1643 | copyright | Springer Basel 2013 |
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