The classification of Kleinian surface groups, I: models and bounds

• 成果类型: Article
• 署名作者: Minsky, Yair
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.171.1
• 发表日期: 2010
• 页码: 1-107
• 关键词: mobius transformations; hyperbolic 3-manifolds; compact submanifolds; geometry; MANIFOLDS; THEOREM; complex; SPACES

摘要

We give the first part of a proof of Thurston's Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a Lipschitz model for the thick part of the corresponding hyperbolic manifold. This enables us to describe the topological structure of the thick part, and to give a priori geometric bounds.