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.

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