Gaussian curvature estimates for the convex level sets of p-harmonic functions

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. © 2010 Wiley Periodicals, Inc.