The Area of Polynomial Images and Preimages

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dc.creatorCrane, Edward
dc.date2003-02-17
dc.date.accessioned2026-07-07T04:55:20Z
dc.date.available2026-07-07T04:55:20Z
dc.descriptionLet 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.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0302189
dc.identifierhttp://arxiv.org/abs/math/0302189
dc.identifierBull. London Math. Soc 36 (2004), 786-792.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66541
dc.subjectComplex Variables
dc.subjectClassical Analysis and ODEs
dc.subjectMetric Geometry
dc.subject30C10 (Primary) 26D05, 30C85 (Secondary)
dc.titleThe Area of Polynomial Images and Preimages
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