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Source: http://www.diva-portal.org/smash/get/diva2:652933/fulltext01.pdf

On page 11 it says: For tangential operators Green's formula becomes

$$(\nabla_{\Sigma}\cdot w ,v)_{\Sigma}=(n_{\Gamma}\cdot w,v)_{\Gamma}-(w,\nabla_{\Sigma}v)_{\Sigma}+(w, Hn_{\Sigma}v)_{\Sigma}$$ where $H$ is the mean curvature of the surface $\Sigma$ with boundary $\partial \Sigma=\Gamma$, $w$ being a vector field and $n$ being the outward pointing unit normal.

Can anyone link me to literature that explains that identity or explain to me how it is being derived?

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