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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On singly-periodic minimal surfaces
with planar ends


Author: Joaquín Pérez
Journal: Trans. Amer. Math. Soc. 349 (1997), 2371-2389
MSC (1991): Primary 53A10, 53C42
MathSciNet review: 1407709
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Abstract: The spaces of nondegenerate properly embedded minimal surfaces in quotients of ${\mathbf R}^3$ by nontrivial translations or by screw motions with nontrivial rotational part, fixed finite topology and planar type ends, are endowed with natural structures of finite dimensional real analytic manifolds. This nondegeneracy is defined in terms of Jacobi functions. Riemann's minimal examples are characterized as the only nondegenerate surfaces with genus one in their corresponding spaces. We also give natural immersions of these spaces into certain complex Euclidean spaces which turn out to be Lagrangian immersions with respect to the standard symplectic structures.


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Additional Information

Joaquín Pérez
Email: jperez@goliat.ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01911-9
PII: S 0002-9947(97)01911-9
Keywords: Minimal surfaces, Jacobi operator
Received by editor(s): November 29, 1995
Additional Notes: Research partially supported by a DGICYT Grant No. PB94-0796.
Article copyright: © Copyright 1997 American Mathematical Society