Minimal translation factorable surfaces in hyperbolic space

The theory of Minimal Surfaces is one of the most interesting subject in mathematics. The study and computation of minimal surfaces has a long history. Lagrange made the first investigation of the minimal surfaces by asking a simple question named as Plateau’s problem which concerns with finding a surface of least area that spans a given fixed one-dimensional contour in three-dimensional Euclidean space. The study of this kind of surfaces has motivated the development of numerous concepts and techniques in the calculus of variations which later have been applied to solving a great quantity of problems in very diverse areas ranging from the study of partial differential equations to topology and even to settling conjectures in relativity. Mathematically, a minimal surface corresponds to the solution of a nonlinear partial differential equation. In this paper, we define two types of Translation-Factorable (T-F) surfaces in the 3-dimensional hyperbolic space. Then, we obtain the complete classification of these surfaces with vanishing mean curvature by solving some differential equations.