Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Bumpy metrics and closed parametrized minimal surfaces in Riemannian manifolds
HTML articles powered by AMS MathViewer

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
Similar Articles
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