The Concavity of the Gaussian Curvature of the Convex Level Sets of $$p$$p-Harmonic Functions with Respect to the Height
The Concavity of the Gaussian Curvature of the Convex Level Sets of $$p$$p-Harmonic Functions with Respect to the Height
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DOI：
10.1007/s40304-014-0025-y
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发表时间：
2013-12
影响因子：
0.9
通讯作者：
Xinan Ma;Wei Zhang
中科院分区：
文献类型：
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作者：
Xinan Ma;Wei Zhang
对于具有严格凸水平集的-调和函数，我们找到了一个由-调和函数的梯度范数和其水平集的高斯曲率的组合而来的辅助函数。我们证明了这个曲率函数相对于-调和函数的高度是凹的。当球上的-调和函数为-格林函数时，该辅助函数是高度的仿射函数。
For the-harmonic function with strictly convex level sets, we find an auxiliary function which comes from the combination of the norm of gradient of the-harmonic function and the Gaussian curvature of the level sets of-harmonic function. We prove that this curvature function is concave with respect to the height of the-harmonic function. This auxiliary function is an affine function of the height when the-harmonic function is the-Green function on ball.