Existence of stable H-surfaces in cones and their representation as radial graphs

InthispaperwestudythePlateauproblemfordisk-typesurfacescontainedinconic regions of R3 and with prescribed mean curvature H . Assuming a suitable growth condition on H , we prove existence of a least energy H -surface X spanning an arbitrary Jordan curve taken in the cone. Then we address the problem of describing such surface X as radial graph when the Jordan curve admits a radial representation. Assuming a suitable monotonicity condition on the mapping λ → λH(λp) and some strong convexity-type condition on the radial projection of the Jordan curve , we show that the H-surface X can be represented as a radial graph.