Goldberg's constants

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.

32 pages, 4 figures

References in corpus (1)

• On the hyperbolic metric of the complement of a rectangular lattice

Cited by in corpus (4)

• Entire functions with two radially distributed values
• Radially distributed values and normal families
• Simultaneous stabilization, avoidance and Goldberg's constants
• Exploiting Algebraic Structure in Global Optimization and the Belgian Chocolate Problem