We give a positive lower bound for the Gaussian curvature of the convex level sets of p-harmonic functions with the Gaussian curvature of the boundary and the norm of the gradient on the boundary. Combining the deformation process, this estimate gives a new approach to studying the convexity of the level sets of the p-harmonic function.

No abstract

Sharp curvature estimates are given for the level sets of a class of p-harmonic functions in two and three dimensional convex rings.

Abstract. In this paper , the author proves a Liouville type theorem for some Hessian entire inequality with sub-lower-critical exponent, via suitable choices of test functions and the argument of integration by parts .

Abstract. In this paper, we introduce a new auxiliary function, and establish the interior C 2 estimate for Monge-Ampère equation in dimension n = 2, which was firstly proved by Heinz [5] by a geometric method.