English

On the minimal diameter of closed hyperbolic surfaces

Geometric Topology 2023-02-22 v1 Probability

Abstract

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

Keywords

Cite

@article{arxiv.1909.12283,
  title  = {On the minimal diameter of closed hyperbolic surfaces},
  author = {Thomas Budzinski and Nicolas Curien and Bram Petri},
  journal= {arXiv preprint arXiv:1909.12283},
  year   = {2023}
}

Comments

9 pages, 4 figures

R2 v1 2026-06-23T11:27:18.505Z