Optimal isoperimetric inequalities for complete proper minimal submanifolds in hyperbolic space

The classical isoperimetric inequality for a domain \(\Sigma \subset \mathbb{R}^{k}\) with smooth boundary \(\partial \Sigma\) is \(\displaystyle{ k^{k}\omega _{ k}\mathrm{Vol}(\Sigma )^{k-1} \leq \mathrm{ Vol}(\partial \Sigma )^{k}, }\) where equality holds if and only if \(\Sigma\) is a ball in \(\mathbb{R}^{k}\).