Gradient Estimates of Mean Curvature Equation with Neumann Boundary   Condition in $ M^n\times \mathbb{R}$
  In this note, we study the prescribed mean curvature equation with   Neumann boundary conditions on Riemannian product manifold $ M^n\times \mathbb{R}$. The main goal is to establish the boundary gradient estimates for solutions by the maximum principle.   As a consequence, we obtain an existence result. 
Jinju Xu and Dekai Zhang
math.DG