On the Edrei-Goldberg-Ostrovskii Theorem for Minimal Surfaces

This paper is devoted to the development of Beckenbach's theory of the meromorphic minimal surfaces. We consider the relationship between the number of separated maximum points of a meromorphic minimal surface and the Baernstein's T*-function. The results of Edrei, Goldberg, Heins, Ostrovskii, Wiman are generalized. We also give examples showing that the obtained estimates are sharp.

Automated summary

This paper is dedicated to the development of Beckenbach's theory on meromorphic minimal surfaces. It examines the relationship between the number of separated maximum points on such surfaces and Baernstein's T*-function. The findings of Edrei, Goldberg, Heins, Ostrovskii, and Wiman are extended, and examples are provided to demonstrate the sharpness of the derived estimates.