منابع مشابه
Geometric properties of hyperbolic geodesics
In the unit disk D hyperbolic geodesic rays emanating from the origin and hyperbolic disks centered at the origin exhibit simple geometric properties. The goal is to determine whether analogs of these geometric properties remain valid for hyperbolic geodesic rays and hyperbolic disks in a simply connected region Ω. According to whether the simply connected region Ω is a subset of the unit disk ...
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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...
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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...
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This sharpens [10], where it was shown that the complex length spectrum of M determines its commensurability class. Suppose M ′ is an arithmetic hyperbolic 3-manifold which is not commensurable to M . Theorem 1.1 implies QL(M) 6= QL(M ′), though by Example 2.1 below it is possible that one of QL(M ′) or QL(M) contains the other. By the length formulas recalled in §2.1 and §2.2, each element of ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2000
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-00-02483-1