TITLE: Area growth of harmonic functions
QUESTION [7 upvotes]: Can one construct a harmonic function $f$ defined in unit disk with condition $f(0)\geq1$ such that area of $\{z\in\mathbb{D}: f(z)>0\}$ is small enough?

REPLY [2 votes]: This question was asked and answered at MathOverflow.
The point of this answer is to provide the link and remove this from the list of unanswered questions.
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