  A space-like surface in Minkowski space-time is minimal if its mean curvature
vector field is zero. Any minimal space-like surface of general type admits
special isothermal parameters - canonical parameters. For any minimal surface
of general type parameterized by canonical parameters we obtain Weierstrass
representations - canonical Weierstrass representations via two holomorphic
functions. We find the expressions of the Gauss curvature and the normal
curvature of the surface with respect to this pair of holomorphic functions. We
find the relation between two pairs of holomorphic functions generating one and
the same minimal space-like surface of general type. The canonical Weierstrass
formulas allow us to establish geometric correspondence between minimal
space-like surfaces of general type and classes of pairs of holomorphic
functions in the Gauss plane.
