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