Picture below is from 1706th page of Zhao Liang's The first eigenvalue of Laplace operator under powers of mean curvature flow.
$M$ is a compact Riemannian manifold. $g_{ij}$ is Riemannian metric, $h_{ij}$ is second fundamental form,$h^{ij}=g^{ip}g^{jq}h_{pq}$, and $H=g^{ij}h_{ij}$. $\nabla$ is Riemannian connect, and $\nabla^pH=g^{pl}\nabla_lH$. $h$ is a constant independ to $x$. Besides, $dim M=n$.
Why there are two gradient at last, I think it should be the inner of two gradient. Besides, how to deal the term with $\frac{2}{n}$ ? I think it should be by integrating by parts, then $\partial_t\sqrt g$ has $\frac{n}{2}$, but I don't know how to calculate $\partial_t\sqrt g$. In fact, I get a complex result without usefull.
