Some geometrical properties of convex level sets of minimal graph on 2-dimensional Riemannian manifolds

Abstract

For the minimal graph defined on two dimensional Riemannian manifolds with constant Gauss curvature, we derive a constant rank theorem on the geodesic curvature of its level sets, and an auxiliary function involving the curvature of the level sets will be found to obtain some differential equalities to study the geometrical properties.