Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations (Journal of Partial Differential Equations, 2012)
We give lower bound estimates for the Gaussian curvature of convex level sets of minimal surfaces and the solutions to semilinear elliptic equations in terms of the norm of boundary gradient and the Gaussian curvature of the boundary.
Keywords: Gaussian curvature estimates; convex level sets; minimal surface; semilinear elliptic equation; maximum principle