2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66541Let p be a monic polynomial in one complex variable and K a measurable subset of the complex plane. In terms of the area of K, we give an upper bound on the area of the preimage of K under p and a lower bound on the area of the image of K under p, (counted with multiplicity). Both bounds are sharp. The former extends an inequality of Polya. The proof uses Carleman's isoperimetric inequality for plane condensers. We include a summary of the necessary potential theory.8 pagesComplex VariablesClassical Analysis and ODEsMetric Geometry30C10 (Primary) 26D05, 30C85 (Secondary)text