2010/02/15 by Graham Smith, Smith, Graham · 1 citation
Mathematics · #35J25 #35J60 #53A10 #53C21 #53C42 #58E12 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.DG #msc:35J25 #msc:35J60 #msc:53A10 #msc:53C21 #msc:53C42 #msc:58E12
paper · pdf · doi:10.48550/arxiv.1002.2982
Formerly "The Plateau Problem in Hadamard Manifolds". Minor changes improving readability and reflecting subsequent developments in the field (esp. arxiv:1008.3545)
openalex publication_date 2010/02/15 · arxiv created 2011/03/16 · arxiv updated 2011/03/17 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We develop a compactness result near the boundary for families of locally convex immersions. We also develop a mod 2 degree theory for immersion of constant (and prescribed) Gaussian curvature with prescribed boundary. These are then used to solve the Plateau problem for immersions of constant (and prescribed) Gaussian curvature in general Hadamard manifolds.