Minimal surface doublings via electrostatics

I'll discuss joint work with Adrian Chu, relating a natural gluing construction for minimal surfaces due to Kapouleas to the variational theory for a Coulomb-type interaction energy for Schroedinger operators. Namely, for the Jacobi operator of a nondegenerate minimal surface, we show that families of nondegenerate critical points of this energy give rise to high-genus minimal surfaces approximating the initial surface with multiplicity two, provided a few key estimates are satisfied. By studying the ground states of this energy, we show that, generically, every minimal surface of index one admits such a doubling, and deduce as a corollary that generic 3-manifolds contain sequences of embedded minimal surfaces with bounded area and arbitrarily large genus.