Interior curvature estimates and the asymptotic plateau problem in hyperbolic space

In this talk, we will begin with definitions of hyperbolic space and De Sitter space. After giving some known results for constant curvature hypersurfaces in hyperbolic space and constant curvature spacelike hypersurfaces in De Sitter space, we will show a strong duality theorem of hyperbolic space and De Sitter space. Finally we will show some applications for this duality theorem. This is a joint work with Bo Guan and Joel Spruck.