Unclouding the sky of negatively curved manifolds
| dc.creator | Parkkonen, Jouni | |
| dc.creator | Paulin, Frederic | |
| dc.date | 2004-02-05 | |
| dc.date.accessioned | 2026-07-07T05:05:09Z | |
| dc.date.available | 2026-07-07T05:05:09Z | |
| dc.description | Let M be a complete simply connected Riemannian manifold, with sectional curvature K bounded above by -1. Under some assumptions on the geometry of the boundary 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 x_0 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 x_0 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. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402073 | |
| dc.identifier | http://arxiv.org/abs/math/0402073 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70070 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53C22; 53C35; 53D25 | |
| dc.title | Unclouding the sky of negatively curved manifolds | |
| dc.type | text |