Mapping properties of analytic functions on the disk

Details Mapping properties of analytic functions on the disk Mapping properties of analytic functions on the disk

2006-01-04

arxiv.org/abs/math/0601080v1

Mathematics

Complex Variables

7 pages

Scientific paper

There is a universal constant $00$ 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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