Interior gradient estimates for mean curvature equations on Riemannian manifolds

In this paper, we study interior gradient estimates for solutions of \[ \operatorname{div}_{M}\left( \frac{\nabla u}{\sqrt{1+|\nabla u|_g^2}} \right) =f(x,\nabla u) \] on a complete Riemannian manifold of dimension $n\ge2$. Under a Ricci curvature lower bound and a Hessian comparison for t