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Mapping properties of analytic functions on the disk

Pietro Poggi-Corradini
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Abstract

There is a universal constant $0 0$ so that the Euclidean area, counting multiplicity, of the portion of $f(\D)$ which lies over the disk $D(f(0),M)$, centered at $f(0)$ and of radius $M$, is strictly less than the area of $D(f(0),M)$. Then $f$ must send $r_0\bar{\D}$ into $D(f(0),M)$. This answers a conjecture of Don Marshall.

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Pietro Poggi-Corradini. 2006-01-04. Mapping properties of analytic functions on the disk. https://arxiv.org/abs/math/0601080

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