A New Proof of Gradient Estimates for Mean Curvature Equations with Oblique Boundary Conditions

In this paper, we will use the maximum principle to give a new proof of the gradient estimates for mean curvature equations with some oblique derivative problems. Specially, we shall give a new proof for the capillary problem with zero gravity in any dimension $n\geq 2$ and Neumann problem in $n=2, 3$ dimensions.