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

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- by John Douglas Moore PDF
- Trans. Amer. Math. Soc.
**358**(2006), 5193-5256 Request permission

Erratum: Trans. Amer. Math. Soc.

**359**(2007), 5117-5123.

## Abstract:

The purpose of this article is to study conformal harmonic maps $f:\Sigma \rightarrow M$, where $\Sigma$ is a closed Riemann surface and $M$ is a compact Riemannian manifold of dimension at least four. Such maps define parametrized minimal surfaces, possibly with branch points. We show that when the ambient manifold $M$ is given a generic metric, all prime closed parametrized minimal surfaces are free of branch points, and are as Morse nondegenerate as allowed by the group of automorphisms of $\Sigma$. They are Morse nondegenerate in the usual sense if $\Sigma$ has genus at least two, lie on two-dimensional nondegenerate critical submanifolds if $\Sigma$ has genus one, and on six-dimensional nondegenerate critical submanifolds if $\Sigma$ has genus zero.## References

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## Additional Information

**John Douglas Moore**- Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
- Email: moore@math.ucsb.edu
- Received by editor(s): February 18, 2004
- Published electronically: July 21, 2006
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**358**(2006), 5193-5256 - MSC (2000): Primary 53C40, 58E12; Secondary 58D15, 58E05
- DOI: https://doi.org/10.1090/S0002-9947-06-04317-0
- MathSciNet review: 2238914