2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219360We show that Bonnesen's isoperimetic defect has a systolic analog for Loewner's torus inequality. The isosystolic defect is expressed in terms of the probabilistic variance of the conformal factor of the metric g with respect to the flat metric of unit area in the conformal class of g.15 pages, 1 figureDifferential GeometryAnalysis of PDEsComplex VariablesMetric Geometry53C23 (Primary); 30F10, 35J60, 58J60 (Secondary)text