Gauss curvature estimates for the convex level sets of a minimal surface immersed in Rn+1Rn+1

This paper is concerned with the Gauss curvature estimates for convex level sets of a minimal surface immersed in Rn+1Rn+1. It is proved that a function involving the Gauss curvature of a level set attains its minimum on the boundary of the minimal surface. As an application, for a minimal graph on a convex ring, a positive lower bound for the Gauss curvature of the convex level set in terms of the Gauss curvature of the boundary and the norm of graph gradient on the boundary can be given.