Bifurcations of minimal surfaces via index theory

Abstract

We present a method for constructing new families of minimal surfaces from an existing minimal surface by applying techniques for proving bifurcations from a simple eigenvalues to the minimal surface equation H = 0 H = 0 . Although there is no explicit free parameter in H = 0 H = 0 , we consider surfaces over compact domains and then vary the effective radius of the domain, which relates the method to the index of a complete minimal surface. We demonstrate the method for the standard catenoid and degree n n Enneper surfaces, although it is certainly more widely applicable.