2010/10/19 by Bo Guan, Joel Spruck, Guan, Bo +1
Mathematics · #58J32 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 53C21 #Secondary 35J65 #math.AP #msc:35J65 #msc:53C21 #msc:58J32
paper · pdf · doi:10.48550/arxiv.1010.4008
arxiv created 2010/10/19 · arxiv updated 2010/10/20
We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f(κ) = σ over (0,1) with a prescribed asymptotic boundary Γ at infinity has at least one solution which is a "vertical graph" over the interior (or the exterior) of Γ. There is uniqueness for a certain subclass of these curvature functions and as σ varies between 0 and 1, these hypersurfaces foliate the two components of the complement of the hyperbolic convex hull of Γ.