Bumpy Riemannian metrics and closed parametrized minimal surfaces in Riemannian manifolds

Details Bumpy Riemannian metrics and closed parametrized minimal surfaces in Riemannian manifolds Bumpy Riemannian metrics and closed parametrized minimal surfaces in Riemannian manifolds

2010-12-17

arxiv.org/abs/1012.3906v2

This is a revision of the article with the same title in Trans. AMS vol. 358 (2006), pp. 5193-5256 with erratum in Trans. AMS

Mathematics

Differential Geometry

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

Scientific paper

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.

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