Bounded geometry for Kleinian groups

• 成果类型: Article
• 署名作者: Minsky, YN
• 署名单位: State University of New York (SUNY) System; Stony Brook University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220100163
• 发表日期: 2001
• 页码: 143-192
• 关键词: curves; complex; deformation; MANIFOLDS; ends

摘要

We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend only on its end invariants. Bounded geometry is a positive lower bound on the lengths of closed geodesics. When the Surface is a once-punctured torus, the coefficients coincide with the continued fraction coefficients associated to the ending laminations.