The non-linear Plateau problem in non-positively curved manifolds
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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.References
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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
- MR Author ID: 741176
- Received by editor(s): August 3, 2010
- Published electronically: October 31, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 1109-1124
- MSC (2010): Primary 58E12; Secondary 35J25, 35J60, 53A10, 53C21, 53C42
- DOI: https://doi.org/10.1090/S0002-9947-2012-05647-9
- MathSciNet review: 3003259