The Non-Liner Dirichlet Problem in Hadamard Manifolds

2009/08/25 by Graham Smith, Smith, Graham · 1 citation
Mathematics · #35J25 #35J60 #53A10 #53C21 #53C42 #58E12 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35J25 #msc:35J60 #msc:53A10 #msc:53C21 #msc:53C42 #msc:58E12

paper · pdf · doi:10.48550/arxiv.0908.3590

arxiv created 2009/08/25 · openalex publication_date 2009/08/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We proof existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Citations

• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
• Moduli of Flat Conformal Structures of Hyperbolic Type
• Calibrated geometries

Cited by

• The non-linear Plateau problem in non-positively curved manifolds

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