Unclouding the Sky of Negatively Curved Manifolds
نویسنده
چکیده
Let M be a complete simply connected Riemannian manifold, with sectional curvature K ≤ −1. Under some assumptions on the geometry of ∂M , which are satisfied for instance if M is a symmetric space, or has dimension 2, we prove that given any family of horoballs in M , and any point x0 outside these horoballs, it is possible to shrink uniformly, by a finite amount depending only on M , these horoballs so that some geodesic ray starting from x0 avoids the shrunk horoballs. As an application, we give a uniform upper bound on the infimum of the heights of the closed geodesics in the finite volume quotients of M .
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