We study the asymptotic static properties of long polymers grafted to a convex surface in a solvent using a variational approach. The equilibrium State is obtained by minimizing the free energy with respect to the free end distribution and the stretching profiles of the polymers. We simplify the minimization by assuming that the stretching profiles of all the chains are the same up to an overall scale factor. This approach when applied to a planar surface reproduces results identical to those obtained by Milner, Witten, and Cates using a self-consistent field approach. For polymers grafted to a cylinder or a sphere, we find two distinct regions : an exclusion zone (r < r(c)) and an end distributed region (r(c) < r < h*). The monomer density profile n(r) in the exclusion zone is found to be consistent with the scaling results based on a blob picture. In the end distributed-region, n(r) is a concave down function and vanishes continuously at the top of the grafting layer. Independently, we found the exact self-consistent solutions for a cylindrical brush in the strong curvature limit, by solving the integral equations of Ball, Marko, Milner, and Witten using the Wiener-Hopf technique. Our simple variational approach produces qualitatively correct features of this exact solution.