Mapping Properties of Analytic Functions on the Disk
نویسنده
چکیده
There is a universal constant 0 < r0 < 1 with the following property. Suppose that f is an analytic function on the unit disk D, and suppose that there exists a constant M > 0 so that the Euclidean area, counting multiplicity, of the portion of f(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 r0D into D(f(0), M). This answers a conjecture of Don Marshall.
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