Existence and uniqueness of CMC parabolic graphs in H3H3 with boundary data satisfying the bounded slope condition

In this work, we investigate the existence of parabolic graphs of constant mean curvature H   in H3H3 whose boundary is given a priori, under hypothesis relating H   with the geometry of the domain and a condition on the boundary data that, by analogy with a similar problem for vertical graphs in R3R3, we denominated it by bounded slope condition.