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

 

The space of complete minimal surfaces
with finite total curvature
as lagrangian submanifold


Authors: Joaquín Pérez and Antonio Ros
Journal: Trans. Amer. Math. Soc. 351 (1999), 3935-3952
MSC (1991): Primary 53A10, 53C42
Published electronically: February 8, 1999
MathSciNet review: 1487630
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Abstract: The space ${\cal M}$ of nondegenerate, properly embedded minimal surfaces in ${\mathbb R}^3$ with finite total curvature and fixed topology is an analytic lagrangian submanifold of ${\mathbb C}^n$, where $n$ is the number of ends of the surface. In this paper we give two expressions, one integral and the other pointwise, for the second fundamental form of this submanifold. We also consider the compact boundary case, and we show that the space of stable nonflat minimal annuli that bound a fixed convex curve in a horizontal plane, having a horizontal end of finite total curvature, is a locally convex curve in the plane ${\mathbb C}$.


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Additional Information

Joaquín Pérez
Affiliation: Departamento de Geometria y Topologia, Facultad de Ciencias, Universidad de Granada, Fuentenueva, 18071, Granada, Spain
Email: jperez@goliat.ugr.es

Antonio Ros
Affiliation: Departamento de Geometria y Topologia, Facultad de Ciencias, Universidad de Granada, Fuentenueva, 18071, Granada, Spain
Email: aros@goliat.ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02250-3
PII: S 0002-9947(99)02250-3
Received by editor(s): April 10, 1997
Published electronically: February 8, 1999
Additional Notes: Research partially supported by a DGYCYT Grant No. PB94-0796.
Article copyright: © Copyright 1999 American Mathematical Society