Minimal surfaces of revolution

In this paper, we will prove that all non-planar minimal surfaces of revolution can be generated by functions of the form f = 1 C cosh(Cx), x ∈ R (as illustrated in Figure 1). We will accomplish this by • Assuming a non-planar minimal surface of revolution exists • Showing that the surface must be given by the above form • Prove that such a surface is indeed minimal. By minimal surface, we mean a surface whose area (in the usual notion of surface area in R) will be increased by any slight perturbation. This definition implies that radius of our surface cannot approach zero as we move along the fixed axis toward infinity, so by translation and scaling, we can assume that some segment of such a surface has boundary of two circles of radius 1 in parallel planes with centers along a common axis.