2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115249On a hyperbolic Riemann surface, given two simple closed geodesics that intersect $n$ times, we address the question of a sharp lower bound $L_n$ on the length attained by the longest of the two geodesics. We show the existence of a surface $S_n$ on which there exists two simple closed geodesics of length $L_n$ intersecting $n$ times and explicitly find $L_n$ for $n\leq 3$.Typos correctedDifferential GeometryGeometric Topology30F45; 30F20text