Characterizations Of Bloch Minimal Surface

In this thesis, we consider the minimal surfaces on the unit disk D and some characterizations of the Bloch minimal surfaces are given. The thesis consists of the following four parts.The first part is focus on reciting the background of the minimal surface, including some known results on the minimal surface, especially for the Bloch minimal surfaces.In the second part, the Bloch minimal surfaces are studied by using the Bergman metric.In the third part, we consider the bounded mean oscillation of the Bloch minimal surfaces in the unit disk.At last, the derivative-free characterization and some other characterizations of the Bloch minimal surfaces are studied.