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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 non-linear Plateau problem in non-positively curved manifolds
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by Graham Smith PDF
Trans. Amer. Math. Soc. 365 (2013), 1109-1124 Request permission

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
  • Andersson L., Barbot T., Béguin F., Zeghib A., Cosmological time versus CMC time in spacetimes of constant curvature, arXiv:math/0701452
  • Stephanie Alexander, Mohammad Ghomi, and Jeremy Wong, Topology of Riemannian submanifolds with prescribed boundary, Duke Math. J. 152 (2010), no. 3, 533–565. MR 2654222, DOI 10.1215/00127094-2010-018
  • Bo Guan and Joel Spruck, The existence of hypersurfaces of constant Gauss curvature with prescribed boundary, J. Differential Geom. 62 (2002), no. 2, 259–287. MR 1988505
  • François Labourie, Un lemme de Morse pour les surfaces convexes, Invent. Math. 141 (2000), no. 2, 239–297 (French). MR 1775215, DOI 10.1007/s002220000069
  • Peter Petersen, Riemannian geometry, 2nd ed., Graduate Texts in Mathematics, vol. 171, Springer, New York, 2006. MR 2243772
  • Harold Rosenberg, Hypersurfaces of constant curvature in space forms, Bull. Sci. Math. 117 (1993), no. 2, 211–239. MR 1216008
  • Smith G., Special Lagrangian curvature, arXiv:math/0506230.
  • Smith G., Moduli of Flat Conformal Structures of Hyperbolic Type, arXiv:0804.0744.
  • Smith G., The Non-Linear Dirichlet Problem in Hadamard Manifolds, arXiv:0908.3590
  • Smith G., Constant Gaussian Curvature Hypersurfaces in Hadamard Manifolds, arXiv: 0912.0248
  • Smith G., The Plateau Problem in Hadamard Manifolds, arXiv:1002.2982
  • Neil S. Trudinger and Xu-Jia Wang, On locally convex hypersurfaces with boundary, J. Reine Angew. Math. 551 (2002), 11–32. MR 1932171, DOI 10.1515/crll.2002.078
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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