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If $k=\nabla\cdot n$, what is the geometric relationship between $k$ and $n$? In terms of size and direction?

Is it true that $n$ is an outward-pointing normal iff $k>0$ and $n$ is inward-pointing iff $k<0$?

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    Mr.Klimpel I assume that the surface is a interface and$k$equals the mean curvature,no twice the mean curvature,but I dont know relationship between them!!! plz help me2012-05-05

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