Tame双曲三维流形的有效钻取与填充
Effective drilling and filling of tame hyperbolic 3-manifolds
摘要：
给出了尖点双曲3-流形的厚部分与其长Dehn填充之间度量变化的有效bilipschitz界。在流形的薄部分，我们给出了短闭测地线复长度变化的有效界。这些结果量化了Brock和Bromberg的填充定理，并将作者以前的结果从有限体积双曲三维流形推广到任何驯服的双曲三维流形。为了证明主要的结果，我们组装工具从克莱因群论到一个模板转移定理的有限体积流形到定理的无限体积流形。我们还证明和应用一个无限体积版本的6-定理。
英文摘要：
We give effective bilipschitz bounds on the change in metric between thick parts of a cusped hyperbolic 3-manifold and its long Dehn fillings. In the thin parts of the manifold, we give effective bounds on the change in complex length of a short closed geodesic. These results quantify the filling theorem of Brock and Bromberg, and extend previous results of the authors from finite volume hyperbolic 3-manifolds to any tame hyperbolic 3-manifold. To prove the main results, we assemble tools from Kleinian group theory into a template for transferring theorems about finite-volume manifolds into theorems about infinite-volume manifolds. We also prove and apply an infinite-volume version of the 6-Theorem.
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