We establish an interior C 2 estimate for k+ 1 convex solutions to Dirichlet problems of k-Hessian equations. We also use such estimate to obtain a rigidity theorem for k+ 1 convex entire solutions of k-Hessian equations in Euclidean space.
We give a proof of the Hard Lefschetz Theorem for orbifolds that does not involve intersection homology. We use a foliated version of the Hard Lefschetz Theorem due to El Kacimi.