On meromorphic functions which are Brody curves

Abstract

We discuss meromorphic functions on the complex plane which are Brody curves regarded as holomorphic maps to P1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {P}}}_1$$\\end{document}, i.e., which have bounded spherical derivative. For some special classes we gave explicit criteria which functions are Brody. We also discuss which divisors of very slow growth may occur as zero divisor of a Brody function and show that there are transcendental entire functions of arbitrarily slow growth which are not Brody.