Let us have Riemannian manifold $M$ with boundary $N.$ Let $F$ be an immersion, such that $F:N\to M$ 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
$$ \int_{N}B(grad(f),grad(f))\Omega, $$
where $\Omega$ is a volume form on $N?$
Is there exist any estimates for this integral?
