On the minimal diameter of closed hyperbolic surfaces

Abstract

We prove that the minimal diameter of a hyperbolic compact orientable surface of genus $g$ is asymptotic to $\log g$ as $g\to \infty$. The proof relies on a random construction, which we analyse using lattice point counting theory and the exploration of random trivalent graphs.

9 pages, 4 figures

Cited by in corpus (3)

• The diameter of random Belyi surfaces
• Systoles and diameters of hyperbolic surfaces
• Hyperbolic manifolds with a large number of systoles