Convergence of freely decomposable Kleinian groups

• 成果类型: Article
• 署名作者: Kim, Inkang; Lecuire, Cyril; Ohshika, Ken'ichi
• 署名单位: Korea Institute for Advanced Study (KIAS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Osaka
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0609-5
• 发表日期: 2016
• 页码: 83-131
• 关键词: hyperbolic structures; algebraic convergence; ending laminations; density conjecture; schottky-groups; surface groups; trees; degenerations; 3-manifolds; MANIFOLDS

摘要

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.