Comparation of values in minimal submanifold

Question

Let $\phi: M^m\to H^n(k)$ be minimal immersion. Show that $$\varepsilon_1\leq\displaystyle\frac{\displaystyle\int_{\{r=s\}}|\nabla^{\top}r|d\lambda(s)}{\displaystyle\int_0^s\sinh^{m-1}\left(\sqrt{-k}t\right)dt}\leq\varepsilon_2,$$ where $\varepsilon_1,\varepsilon_2>0$, $H$ is hyperbolic space with curvature $k<0$ and $r$ is distance function in $H$.