English

Bumpy Riemannian metrics and closed parametrized minimal surfaces in Riemannian manifolds

Differential Geometry 2011-05-05 v2

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.

Keywords

Cite

@article{arxiv.1012.3906,
  title  = {Bumpy Riemannian metrics and closed parametrized minimal surfaces in Riemannian manifolds},
  author = {John Douglas Moore},
  journal= {arXiv preprint arXiv:1012.3906},
  year   = {2011}
}

Comments

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