Convexity of the smallest principal curvature of the convex level sets of some quasi-linear elliptic equations with respect to the height

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For the p-harmonic function with strictly convex level sets, we find a test function which comes from the combination of the norm of gradient of the p-harmonic function and the smallest principal curvature of the level sets of p-harmonic function. We prove that this curvature function is convex with respect to the height of the p-harmonic function. This test function is an affine function of the height when the p-harmonic function is the p-Green function on the ball. For the minimal graph, we obtain a similar results.