Mathematics – Complex Variables
Scientific paper
2011-11-09
Mathematics
Complex Variables
32 pages, 4 figures
Scientific paper
We study two extremal problems of geometric function theory introduced by A. A. Goldberg in 1973. For one problem we find the exact solution, and for the second one we obtain partial results. In the process we study the lengths of hyperbolic geodesics in the twice punctured plane, prove several results about them and make a conjecture. Goldberg's problems have important applications to control theory.
Bergweiler Walter
Eremenko Alexandre
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