Gráficos de curvatura média constante com bordo prescrito satisfazendo a condição de declividade limitada

Abstract

We study problems of existence and uniqueness of constant mean curvature surfaces with prescribed boundary satisfying the bounded slope condition. The surfaces are given as Euclidean graphs in R3 and as parabolic graphs in H3, over bounded domains contained in totally geodesic surfaces in these ambients, or moreover, as radial graphs over bounded domains contained in S2.