# Report

## Numerical solution of the omitted area problem of univalent function theory

Abstract:
The omitted area problem was posed by Goodman in 1949: what is the maximum area $A^*$ of the unit disk D that can be omitted by the image of the unit disk under a univalent function normalized by f(0)=0 and f'(0)=1? The previous best bounds were 0.240005$\pi$ < $A^*$ < .31$\pi$. Here the problem is addressed numerically and it is found that these estimates are slightly in error. To ten digits, the correct value appears to be $A^*$ = 0.2385813248$\pi$.

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### Authors

Publisher:
Unspecified
Publication date:
2001-12-01
UUID:
uuid:0d3832e1-1677-4e83-8f5a-f0464e5f8b27
Local pid:
oai:eprints.maths.ox.ac.uk:1228
Deposit date:
2011-05-31