A sharper bound on the minimal possible diameter of a closed hyperbolic surface

TL;DR

This paper establishes an improved upper bound on the minimal diameter of closed hyperbolic surfaces, showing it grows roughly logarithmically with genus, refined by additional logarithmic factors.

Contribution

The authors provide a sharper upper bound on the minimal diameter of closed hyperbolic surfaces, advancing understanding of geometric properties related to surface genus.

Findings

Minimal diameter is at most log(g) + 25 log log(g) + O(1)

The bound improves previous estimates on hyperbolic surface diameters

The result links surface genus to geometric diameter growth

Abstract

We prove that the minimal possible diameter of a closed hyperbolic surface of genus $g$ is at most $\log(g)+25 \log \log(g) + O(1)$.