Goldberg's constants
Complex Variables
2018-01-08 v1 Optimization and Control
Abstract
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.
Cite
@article{arxiv.1111.2296,
title = {Goldberg's constants},
author = {Walter Bergweiler and Alexandre Eremenko},
journal= {arXiv preprint arXiv:1111.2296},
year = {2018}
}
Comments
32 pages, 4 figures