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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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    Do you mean to say $k = \nabla N$?2012-05-04
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    Please take a moment to consider what *specific* question you want to ask.2012-05-04
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    I mean that "∇.N"2012-05-04
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    Are you assuming an implicitly defined surface here? I would use a local orthogonal coordinate system to see that $\nabla\cdot n$ is independent of the implicit surface equation, and equals the sum of the two principal curvatures. This implies that your $k$ equals twice the mean curvature. I think $n$ must be outward-pointing normal if you want to get the "correct" sign for the mean curvature.2012-05-04
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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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