Convergence of freely decomposable Kleinian groups
Convergence of freely decomposable Kleinian groups
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可自由分解的克莱因群的收敛性
DOI：
10.1007/s00222-015-0609-5
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发表时间：
2016
影响因子：
3.1
通讯作者：
Ken'ichi Ohshika
中科院分区：
文献类型：
--
作者：
Inkang Kim;Cyril Lecuire;Ken'ichi Ohshika
考虑具有可压缩边界的紧致可定向双曲3-流形。假设给定一个几何有限双曲度量序列，其保形边界结构在无穷远处发散为射影层合。证明了如果该极限投影层合是双不可压缩的，则该序列在变形空间中具有紧闭性。由此推广了瑟斯顿的双极限定理，并肯定地解决了瑟斯顿关于函数群收敛性的猜想。
We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination. We prove that if this limit projective lamination is doubly incompressible, then the sequence has compact closure in the deformation space. As a consequence we generalise Thurston’s double limit theorem and solve his conjecture on convergence of function groups affirmatively.