Systole et rayon maximal des variétés hyperboliques non compactes

Abstract

We bound two global invariants of cusped hyperbolic manifolds: the length of the shortest closed geodesic (the systole), and the radius of the biggest embedded ball (the inradius). We give an upper bound for the systole, expressed in terms of the dimension and simplicial volume. We find a positive lower bound on the inradius independent of the dimension. These bounds are sharp in dimension 3, realized by the Gieseking manifold. It provides a new characterization of this manifold.

26 pages, 15 figures

References in corpus (4)

• Systoles of Hyperbolic Manifolds
• The centered dual and the maximal injectivity radius of hyperbolic surfaces
• Geometric limits of knot complements
• Systoles and Dehn surgery for hyperbolic 3-manifolds

Cited by in corpus (5)

• On the convergence of arithmetic orbifolds
• Systoles and Dehn surgery for hyperbolic 3-manifolds
• Hyperbolic manifolds with a large number of systoles
• Hyperbolic 3-manifolds with large kissing number
• The maximal injectivity radius of hyperbolic surfaces with geodesic boundary