  We construct a weakly complete flat surface in hyperbolic 3-space having a
pair of hyperbolic Gauss maps both of whose images are contained in an
arbitrarily given open disc in the ideal boundary of H^3. This construction is
accomplished as an application of the minimal surface theory. This looks an
interesting phenomenon if one comparing the fact that there are no complete
minimal (resp. constant mean curvature one) surfaces in R^3 (resp. H^3) having
bounded Gauss maps (resp. bounded hyperbolic Gauss maps).
