## Mapping properties of analytic functions on the disk

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- by Pietro Poggi-Corradini
- Proc. Amer. Math. Soc.
**135**(2007), 2893-2898 - DOI: https://doi.org/10.1090/S0002-9939-07-08823-5
- Published electronically: May 8, 2007
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## Abstract:

There is a universal constant $0<r_0<1$ with the following property. Suppose that $f$ is an analytic function on the unit disk $\mathbb D$, and suppose that there exists a constant $M>0$ so that the Euclidean area, counting multiplicity, of the portion of $f(\mathbb D)$ 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 $r_0\overline {\mathbb D}$ into $D(f(0),M)$. This answers a conjecture of Don Marshall.## References

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## Bibliographic Information

**Pietro Poggi-Corradini**- Affiliation: Department of Mathematics, Cardwell Hall, Kansas State University, Manhattan, Kansas 66506
- Email: pietro@math.ksu.edu
- Received by editor(s): January 3, 2006
- Received by editor(s) in revised form: June 1, 2006
- Published electronically: May 8, 2007
- Communicated by: Juha M. Heinonen
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**135**(2007), 2893-2898 - MSC (2000): Primary 30C55
- DOI: https://doi.org/10.1090/S0002-9939-07-08823-5
- MathSciNet review: 2317966