摘要
For the p-harmonic function with strictly convex level sets,we find an auxiliary function which comes from the combination of the norm of gradient of the p-harmonic function and the Gaussian curvature of the level sets of p-harmonic function.We prove that this curvature function is concave with respect to the height of the p-harmonic function.This auxiliary function is an affine function of the height when the p-harmonic function is the p-Green function on ball.
基金
Research of the first author was supported by NSFC and Wu Wen-Tsun Key Laboratory of Mathematics.We finished this paper in the winter of 2009 as a part of the thesis of the second author in University of Science and Technology of China.
