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As a definition, I was told that for a surface in 3D,

$ 2H = -\nabla \cdot \nu$

where $H$ is the mean curvature and $\nu$ is the normal unit vector. In some results that I am studying, the factor 2 always disappears... Is this normal ? can we ignore the factor 2 and consider the definition "up to a constant" ?

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Both

$$H = -\nabla \cdot \nu, \ \ \ H =-\frac{1}{2} \nabla \cdot \nu$$

are used in the literature. The former is more convenient (don't need to remind ourselves that there is a two) while the latter has the advantage that $H=1$ when the surface is the unit sphere. Just pick one and be careful.

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