In this talk, we will begin with definitions of hyperbolic space. After giving some known results for constant curvature hypersurfaces in hyperbolic space, we will state our main result and also give an idea of how it's proven. If we have time, we will show a strong duality theorem of hyperbolic space and De Sitter space, and also we will show some applications for this duality theorem. This is a joint work with Bo Guan and Joel Spruck.