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

2010/04/02 by Graham Smith, Smith, Graham
Engineering · Mathematics · #35J25 #35J60 #53A10 #53C21 #53C42 #58E12 #Differential Geometry (math.DG) #Elasticity and Wave Propagation #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.DG #msc:35J25 #msc:35J60 #msc:53A10 #msc:53C21 #msc:53C42 #msc:58E12

paper · pdf · doi:10.48550/arxiv.1004.0374

This paper complements the results of arXiv:0908.3590.

arxiv created 2010/04/02 · openalex publication_date 2010/04/02 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Non-Liner Dirichlet Problem in Hadamard Manifolds

Related

• The Perron Method and the Non-Linear Plateau Problem
• The Plateau problem for convex curvature functions
• Plateau Stein Manifolds
• Hyperbolic Plateau problems
• Some fully nonlinear problems on manifolds with boundary of negative admissible curvature