Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives
نویسندگان
چکیده
منابع مشابه
Hyperbolic Cone-manifolds, Short Geodesics, and Schwarzian Derivatives
With his hyperbolic Dehn surgery theorem and later the orbifold theorem, Thurston demonstrated the power of using hyperbolic cone-manifolds to understand complete, non-singular hyperbolic 3-manifolds. Hodgson and Kerckhoff introduced analytic techniques to the study of cone-manifolds that they have used to prove deep results about finite volume hyperbolic 3-manifolds. In this paper we use Hodgs...
متن کاملSimple Closed Geodesics in Hyperbolic 3-Manifolds
This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only example of a complete nonelementary orientable hyperbolic 3-manifold that does not contain a simple closed geodesic. We do not assume that the manifold is geometrically finite or that it has finitely generated fundament...
متن کاملDrilling long geodesics in hyperbolic 3-manifolds
Given a complete hyperbolic 3-manifold one often wants to compare the original metric to a complete hyperbolic metric on the complement of some simple closed geodesic in the manifold. In some cases this can be done by interpolating between the two metrics using hyperbolic cone-manifolds. We refer to such a deformation as drilling and results which compare the geometry of the original manifold t...
متن کاملNon-simple Geodesics in Hyperbolic 3-manifolds
Chinburg and Reid have recently constructed examples of hyperbolic 3manifolds in which every closed geodesic is simple. These examples are constructed in a highly non-generic way and it is of interest to understand in the general case the geometry of and structure of the set of closed geodesics in hyperbolic 3-manifolds. For hyperbolic 3-manifolds which contain an immersed totally geodesic surf...
متن کاملDeformations of Hyperbolic Cone Manifolds
We show that any compact orientable hyperbolic cone manifold with cone angles at most can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity This together with the local rigidity by Hodgson and Kerckho implies the global rigidity for compact orientable hyperbolic cone manifolds under the same angle assumption
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2004
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-04-00462-x