The areas of polynomial images and pre-images

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)

Abstract

Let p be a monic complex polynomial of degree n, and let K be a measurable subset of the complex plane. Then the area of p(K), counted with multiplicity, is at least pi.n(Area(K)/pi)^n, and the area of the pre-image of K under p is at most (pi^(1-1/n)).(Area(K))^(1/n). Both bounds are sharp. The special case of the pre-image result in which K is a disc is a classical result, due to Polya. The proof is based on Carleman's classical isoperimetric inequality for plane condensers.
Translated title of the contributionThe areas of polynomial images and pre-images
Original languageEnglish
Pages (from-to)786 - 792
Number of pages7
JournalBulletin of the London Mathematical Society
Volume36 (6)
DOIs
Publication statusPublished - Nov 2004

Bibliographical note

Publisher: Cambridge University Press
Other identifier: IDS Number: 874KE

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