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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 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The space of complete minimal surfaces with finite total curvature as lagrangian submanifold
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by Joaquín Pérez and Antonio Ros PDF
Trans. Amer. Math. Soc. 351 (1999), 3935-3952 Request permission

Abstract:

The space $\mathcal {M}$ 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
  • Received by editor(s): April 10, 1997
  • Published electronically: February 8, 1999
  • Additional Notes: Research partially supported by a DGYCYT Grant No. PB94-0796.
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 3935-3952
  • MSC (1991): Primary 53A10, 53C42
  • DOI: https://doi.org/10.1090/S0002-9947-99-02250-3
  • MathSciNet review: 1487630