The Mathematical Institute, University of Oxford, Eprints Archive

Numerical solution of the omitted area problem of univalent function theory

Banjai, Lehel and Trefethen, Lloyd N. (2001) Numerical solution of the omitted area problem of univalent function theory. Technical Report. Unspecified. (Submitted)

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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$\pi$.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Functions of a complex variable
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1228
Deposited By:Lotti Ekert
Deposited On:20 May 2011 09:18
Last Modified:20 May 2011 09:18

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