Systoles and kissing numbers of finite area hyperbolic surfaces

Abstract

We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main result is a bound which only depends on the topology of the surface and which grows subquadratically in the genus.

A minor mistake and a computation fixed, small changes in the exposition. 23 pages, 13 figures

References in corpus (3)

• Random regular graphs and the systole of a random surface
• Systoles and kissing numbers of finite area hyperbolic surfaces
• A Note on Riemann Surfaces of Large Systole

Cited by in corpus (7)

• Systoles and kissing numbers of finite area hyperbolic surfaces
• Fractional Calderón problem on a closed Riemannian manifold
• The extremal length systole of the Bolza surface
• Construction of hyperbolic Riemann surfaces with large systoles
• Hyperbolic manifolds with a large number of systoles
• Hyperbolic 3-manifolds with large kissing number
• Systoles on punctured spheres