Interior Gradient Estimates and Existence Theorems for Constant Mean Curvature Graphs in Mn × R

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Infinite boundary value problems for constant mean curvature graphs in ℍ2 × ℝ and S2 × ℝ (2009, methodology): “that of [9] using the existence theory and interior gradient estimates of [ 10 ]”
The Plateau problem for marginally outer trapped surfaces (2007, methodology): “Simon (see [K86], [KS88], and also [ Sp07 ] for the method on Riemannian manifolds) to show how interior gradient estimates for solutions u of the approximate Jang’s equation (H+tr(p))u = tu follow from one-sided oscillation bounds.”
The half-space property and entire positive minimal graphs in M x R (2012, methodology): “The method presented here sharpens the result of [17] in that no control of injectivity radius is needed.”