Minimal diameter of a closed hyperbolic surface of genus g is at most log(g) + 25 log log(g) + O(1).
Petites valeurs propres du laplacien sur une surface de R iemann compacte et graphes
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A sharper bound on the minimal possible diameter of a closed hyperbolic surface
Minimal diameter of a closed hyperbolic surface of genus g is at most log(g) + 25 log log(g) + O(1).