MathDB
Miklós Schweitzer 1960- Problem 3

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November 18, 2015
college contests

Problem Statement

3. Let f(z)f(z) with f(0)=1f(0)=1 be regular in the unit disk and let
[∂2∣f(z)∣∂x∂y]z=0=1\left [\frac{\partial^2 \mid f(z)\mid}{\partial x\partial y} \right ] _{z=0} =1.
Show thatthe area of the image of the unit disk by w=f(z)w= f(z) (taken with multiplicity) is not less than 12\frac {1} {2} .(f. 6)
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