2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121341We equip many non compact non simply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly non generic property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how.To appear soon in American Journal of Mathematics, a journal published by The Johns Hopkins University PressDifferential Geometry53C20, 49Q20text