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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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Complete linear Weingarten surfaces of Bryant type. A Plateau problem at infinity
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by José Antonio Gálvez, Antonio Martínez and Francisco Milán PDF
Trans. Amer. Math. Soc. 356 (2004), 3405-3428 Request permission

Abstract:

In this paper we study a large class of Weingarten surfaces which includes the constant mean curvature one surfaces and flat surfaces in the hyperbolic 3-space. We show that these surfaces can be parametrized by holomorphic data like minimal surfaces in the Euclidean 3-space and we use it to study their completeness. We also establish some existence and uniqueness theorems by studing the Plateau problem at infinity: when is a given curve on the ideal boundary the asymptotic boundary of a complete surface in our family? and, how many embedded solutions are there?
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Additional Information
  • José Antonio Gálvez
  • Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
  • Email: jagalvez@ugr.es
  • Antonio Martínez
  • Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
  • Email: amartine@ugr.es
  • Francisco Milán
  • Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
  • Email: milan@ugr.es
  • Received by editor(s): November 11, 2002
  • Published electronically: April 26, 2004
  • Additional Notes: This research was partially supported by MCYT-FEDER Grant No. BFM2001-3318 and Junta de Andalucía CEC: FQM0804
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 3405-3428
  • MSC (2000): Primary 53C42; Secondary 53A35
  • DOI: https://doi.org/10.1090/S0002-9947-04-03592-5
  • MathSciNet review: 2055739