Gradient estimates for Neumann boundary value problem of Monge-Ampère type equations on Riemannian manifolds

In this paper, we consider the Monge-Ampère type equations with the Neumann boundary conditions on Riemannian manifolds. Our main result is the gradient estimates for the degenerate elliptic solution, which is the extension of the main theorem in Jiang et al. (2016) from Rn to Riemannian manifolds.