The Neumann problem of Hessian quotient equation

In this talk, we introduce the Neumann problem of Hessian quotient equation. We obtain some important inequalities of Hessian quotient operators, and global C^2 estimates of the Neumann problem of Hessian quotient equations. By the method of continuity, we establish the existence theorem

of k-admissible solutions of the Neumann problem of Hessian quotient equations. Also, we can use the parabolic equation method to study the Neumann problem of Hessian quotient equations. These are joint works with Xinan Ma and Dekai Zhang.