I am reading a paper, where an integral of a divergence over a closed surface is used without proof.

$\oint_S \nabla \cdot \vec{v}(\vec{r}) = 0$,

where $\vec{v}$ is tangential to the surface ($\vec{v}(r)\cdot \vec{n}(\vec{r}) = 0$)

I have looked at vector calculus identities and Green theorems and can't seem to find the expression I need. Any suggestions?


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