Please note special day (Thursday), time and location.  In this talk, we will begin with the definition of hyperbolic space. After giving some known results for constant curvature hypersurfaces in hyperbolic space, we will state our main result and also sketch how it's proven. If we have time, we will show a strong duality theorem of hyperbolic space and De Sitter space. We will also show some applications of this duality theorem. This work is joint with Bo Guan and Joel Spruck.