Bumpy Riemannian metrics and closed parametrized minimal surfaces in Riemannian manifolds

Abstract

This article proves that if M is a smooth manifold of dimension at least four, then for generic choice of metric on M, all prime parametrized minimal surfaces in M are free of branch points and lie on nondegenerate critical submanifolds for the two-variable energy function which have the same dimension as the group of complex automorphisms of the domain Riemann surface.

78 pages, 1 figure; revised arguments in sections 7.3, 7.4 and 9