We prove that the minimal diameter of a closed orientable hyperbolic surface of genus is asymptotic to as . The proof relies on a random construction, which we analyze using lattice-point counting theory and the exploration of random trivalent graphs.
"On the minimal diameter of closed hyperbolic surfaces." Duke Math. J. 170 (2) 365 - 377, 1 February 2021. https://doi.org/10.1215/00127094-2020-0083