Let $(M,g)$ be a closed Riemannian manifold, $\Theta$ be a calibration n-form, and $p\in M$. Assume that the sectional curvature $K_{g}$ satisfies

$$\sup_{B_{g}(p,2\pi)}K_{g}\leq 1,$$

and there is a submanifold $L$ calibrated by $\Theta$ such that $p\in L$. Then

$$Vol_{g}(B_{g}(p,r)\cap L)\geq Vol_{h_{1}}(B_{h_{1}}(r)),$$

for any $r\leq\min\{i_{g}(p),\pi\}$, where $h_{1}$ denotes the standard metric on $S^{n}$ with constant curvature 1, and $B_{h_{1}}(r)$ denotes a metric $r$-ball in $S^{n}$.