Integral of second fundamental form

Let us have Riemannian manifold M with boundary N. Let F be an immersion, such that F:NM and B be a second fundamental form on N relative to F. And let f be a function on N.

How we can calculate integral

NB(grad(f),grad(f))Ω,

where Ω is a volume form on N?

Is there exist any estimates for this integral?

Answer

Attribution
Source : Link , Question Author : Dozzy Cooper , Answer Author : Community

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