2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102251Let G be a planar graph with polynomial growth and isoperimetric dimension bigger than 1. Then the critical p for Bernoulli percolation on G satisfies p<1.5 pages. New version includes a proof of the existence of a dual graph of the type necessary for the proof. Accepted to Rev. Math. IberoamericanaProbabilityCombinatorics60K35, 82B43, 05C10text