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Titlebook: Complex Kleinian Groups; Angel Cano,Juan Pablo Navarrete,José Seade Book 2013 Springer Basel 2013 Kleinian groups.complex hyperbolic geome

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发表于 2025-3-21 18:34:54 | 显示全部楼层 |阅读模式
书目名称Complex Kleinian Groups
编辑Angel Cano,Juan Pablo Navarrete,José Seade
视频videohttp://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Titlebook: Complex Kleinian Groups;  Angel Cano,Juan Pablo Navarrete,José Seade Book 2013 Springer Basel 2013 Kleinian groups.complex hyperbolic geome
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
doihttps://doi.org/10.1007/978-3-0348-0481-3
isbn_softcover978-3-0348-0805-7
isbn_ebook978-3-0348-0481-3Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightSpringer Basel 2013
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发表于 2025-3-22 01:08:27 | 显示全部楼层
Kommentar zu C. Knill und D. Lehmkuhl on its complement is properly discontinuous, which is useful for studying geometric properties of the group. Yet, this may not be the largest region where the action is properly discontinuous. There is also the region of equicontinuity, which provides a set where we can use the powerful tools of analysis to study the group action.
发表于 2025-3-22 06:31:08 | 显示全部楼层
The Limit Set in Dimension 2, on its complement is properly discontinuous, which is useful for studying geometric properties of the group. Yet, this may not be the largest region where the action is properly discontinuous. There is also the region of equicontinuity, which provides a set where we can use the powerful tools of analysis to study the group action.
发表于 2025-3-22 10:41:27 | 显示全部楼层
Book 2013rk 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, the
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发表于 2025-3-22 20:35:24 | 显示全部楼层
https://doi.org/10.1007/978-3-662-54308-5morphisms of . can also be classified into the three types of elliptic, parabolic and loxodromic (or hyperbolic) elements, according to their geometry and dynamics. This classification can be also done algebraically, in terms of their trace.
发表于 2025-3-22 22:02:18 | 显示全部楼层
Staatsentwicklung und PolicyforschungSchottky group. On the other hand, the limit sets of Schottky groups have rich and fascinating geometry and dynamics, which has inspired much of the current knowledge we have about fractal sets and 1-dimensional holomorphic dynamics.
发表于 2025-3-23 01:24:43 | 显示全部楼层
发表于 2025-3-23 08:13:17 | 显示全部楼层
Geometry and Dynamics of Automorphisms of ,,morphisms of . can also be classified into the three types of elliptic, parabolic and loxodromic (or hyperbolic) elements, according to their geometry and dynamics. This classification can be also done algebraically, in terms of their trace.
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