Abstract: Motivated by the isometric embedding problem and fully nonlinear PDE theory, we study the

apriori estimate for scalar curvature equations. Joint with Prof. Pengfei Guan, we proved there is an interior

second order estimate for isometrically embedded hypersurfaces. Moreover, I will talk about my observation

in three-dimensional hypersurface with positive scalar curvature which gives affirmatively answer to the interior second order estimate to this fully nonlinear PDE in 3-dimension.