Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Complete linear Weingarten surfaces of Bryant type. A Plateau problem at infinity


Authors: José Antonio Gálvez, Antonio Martínez and Francisco Milán
Journal: Trans. Amer. Math. Soc. 356 (2004), 3405-3428
MSC (2000): Primary 53C42; Secondary 53A35
Published electronically: April 26, 2004
MathSciNet review: 2055739
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C42, 53A35

Retrieve articles in all journals with MSC (2000): 53C42, 53A35


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

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03592-5
PII: S 0002-9947(04)03592-5
Keywords: Hyperbolic 3-space, Weingarten surfaces, Plateau problem, Weierstrass data.
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
Article copyright: © Copyright 2004 American Mathematical Society