On the L Cohomology of a Convex Cocompact Hyperbolic Manifold

نویسنده

  • Xiaodong Wang
چکیده

We prove a vanishing theorem for a convex cocompact hyperbolic manifold, which relates its L cohomology and the Hausdorff dimension of its limit set. The borderline case is shown to characterize the manifold completely.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the L2-cohomology of a Convex Cocompact Hyperbolic Manifold

We prove a vanishing theorem for a convex cocompact hyperbolic manifold which relates its L2-cohomology and the Hausdorff dimension of its limit set. The borderline case is shown to characterize the manifold completely.

متن کامل

Geodesic planes in the convex core of an acylindrical 3-manifold

Let M be a convex cocompact, acylindrical hyperbolic 3-manifold of infinite volume, and let M∗ denote the interior of the convex core of M . In this paper we show that any geodesic plane inM∗ is either closed or dense. We also show that only countably many planes are closed. These are the first rigidity theorems for planes in convex cocompact 3-manifolds of infinite volume that depend only on t...

متن کامل

Holography and the Geometry of Certain Convex Cocompact Hyperbolic 3-Manifolds

Applying the idea of AdS/CFT correspondence, Krasnov [Kra00] studied a class of convex cocompact hyperbolic 3-manifolds. In physics literature they are known as Euclidean BTZ black holes. Mathematically they can be described as H/Γ, where Γ ⊂ PSL(2,C) is a Schottky group. His main result, roughly speaking, identifies the renormalized volume of such a manifold with the action for the Liouville t...

متن کامل

On Ergodic Properties of the Burger-roblin Measure

In this note we intend to describe some dynamical properties of oneparameter unipotent flows on the frame bundle of a convex cocompact hyperbolic 3-manifold. Much effort and study have been done in the case of manifolds with finite volume, and quite a rich theory is developed in this case. The case of infinite volume manifolds, however, is far less understood. The goal here is to highlight some...

متن کامل

Fe b 20 09 GEOMETRIC LIMITS OF KNOT COMPLEMENTS

We prove that any complete hyperbolic 3–manifold with finitely generated fundamental group, with a single topological end, and which embeds into S is the geometric limit of a sequence of hyperbolic knot complements in S. In particular, we derive the existence of hyperbolic knot complements which contain balls of arbitrarily large radius. We also show that a complete hyperbolic 3–manifold with t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008