2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71554We show that round hemispheres are the only compact 2 dimensional Riemannian manifolds (with or without boundary) such that almost every pair of complete geodesics intersect once and only once. We prove this by establishing a sharp isoperimetric inequality for surfaces with boundary such that every pair of geodesics have at most one interior intersection point.Latex, 4 pagesDifferential GeometryMetric Geometry53C22; 53C24; 53C65; 53A99; 53C20text