Unclouding the sky of negatively curved manifolds

dc.creatorParkkonen, Jouni
dc.creatorPaulin, Frederic
dc.date2004-02-05
dc.date.accessioned2026-07-07T05:05:09Z
dc.date.available2026-07-07T05:05:09Z
dc.descriptionLet 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.description32 pages
dc.identifierhttps://arxiv.org/abs/math/0402073
dc.identifierhttp://arxiv.org/abs/math/0402073
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70070
dc.subjectDifferential Geometry
dc.subjectMetric Geometry
dc.subject53C22; 53C35; 53D25
dc.titleUnclouding the sky of negatively curved manifolds
dc.typetext

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