Gauss curvature estimates for minimal graphs
Geodesics and soap bubbles in surfaces.
Geometric Properties of Minimal Surfaces with Free Boundaries.
Global boundedness, interior gradient estimates, and boundary regularity for the mean curvature equation with boundary conditions.
Gradient estimates and Harnack inequalities for solutions to the minimal surface equation
A gradient estimate for solutions to the minimal surface equation can be proved by Partial Differential Equations methods, as in [2]. In such a case, the oscillation of the solution controls its gradient. In the article presented here, the estimate is derived from the Harnack type inequality established in [1]. In our case, the gradient is controlled by the area of the graph of the solution or by the integral of it. These new results are similar to the one announced by Ennio De Giorgi in [3].
Gradient Estimates and Mean Curvatures.
Gyroids of constant mean curvature.