In this paper we use the polymer adsorption theory of Scheutjens and Fleer to describe polymer brushes at spherical and cylindrical surfaces that are immersed in a low molecular weight solvent. We analyze the volume fraction profiles of such brushes, focusing our attention on spherical brushes in athermal solvents. These are shown to generally consist of two parts : a power law-like part and a part that is consistent with a parabolic potential energy profile of the polymer segments. Depending on the curvature of the surface, one of these two parts is more important, or may even dominate completely. We especially consider the distribution of the free end segments and the possible existence of a "dead zone" for these segments. Such a dead zone is actually found and is seen to follow a scaling law in the case of large curvatures. Furthermore, the effect of diminishing the solvent quality is considered for both the total volume fraction profile and the distribution of the end segments.