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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 non-linear Plateau problem in non-positively curved manifolds


Author: Graham Smith
Journal: Trans. Amer. Math. Soc. 365 (2013), 1109-1124
MSC (2010): Primary 58E12; Secondary 35J25, 35J60, 53A10, 53C21, 53C42
Published electronically: October 31, 2012
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Abstract: Using the Perron method, we prove the existence of hypersurfaces of prescribed special Lagrangian curvature with prescribed boundary inside complete Riemannian manifolds of non-positive curvature.


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Additional Information

Graham Smith
Affiliation: Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, Brazil 22460-320

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05647-9
PII: S 0002-9947(2012)05647-9
Keywords: Dirichlet problem, special Lagrangian curvature, non-linear elliptic PDEs
Received by editor(s): August 3, 2010
Published electronically: October 31, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.