Properly embedded surfaces with prescribed mean curvature in H2 x R

The aim of this paper is to extend classic results of the theory of constant mean curvature surfaces in the product space H-2 x R to the class of immersed surfaces whose mean curvature is given as a C-1 function depending on their angle function. We cover topics such as the existence of a priori curvature and height estimates for graphs and a structure-type result, which classifies properly embedded surfaces with finite topology and at most one end.