Global $C^2$ estimates for convex solutions of curvature equations

Pengfei Guan, Changyu Ren, Zhizhang Wang

We establish $C^2$ a priori estimate for convex hypersurfaces whose principal curvatures $\kappa =({\kappa }_1,...,{\kappa }_n)$ satisfying Weingarten curvature equation ${\sigma }_k(\kappa (X))=f(X,\nu (X))$. We also…