The limit set intersection theorem for finitely generated Kleinian groups
The limit set intersection theorem for finitely generated Kleinian groups
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DOI：
10.4310/mrl.1996.v3.n5.a9
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发表时间：
1996
影响因子：
1
通讯作者：
James W. Anderson
中科院分区：
文献类型：
--
作者：
James W. Anderson
The proof of the Theorem proceeds by showing that it holds in some special cases involving Kleinian groups with connected limit sets, and then extending to the general case by using a decomposition argument based on the Klein-Maskit combination theorems and a careful tracking of the limit points resulting from this decomposition. We discuss various well-behaved classes of limit points in Section 2. We describe the decomposition results taken from Klein-Maskit combination theory in Section 3. We apply the decomposition results to a special subclass of groups in Section 4. We then complete the proof in Section 5. In Section 6, we discuss the extension of Theorem 5.4 to groups with torsion, the difficulty with extending to groups with parabolics, and make note of a reduction of the Ahlfors measure conjecture.
