Maximal domains for entire functions (Q1317274)

This paper could perhaps be described as an interesting study of geometric-topological properties of analytic functions of the plane. The notions used in this work include terms such as tiling and Dirichlet maximal domain for which the author gives precise definitions. Some of the notions used are illuminated by several examples and figures. Although the main focus is in the plane case some arguments are carried out for discrete open maps in the Euclidean \(n\)-space. Then specializing to the two-dimensional case, the author introduces a class of maps for which a Picard type theorem holds and he studies asymptotic values of such maps.