The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition

In this paper, we focus on a marginally trapped submanifold f:Σⁿ → Mⁿ⁺²₁ in a Lorentzian manifold Mⁿ⁺²₁. We show that f lies in a certain null hypersurface Nfⁿ⁺¹ in Mⁿ⁺²₁ and f has a locally volume-maximizing property in Nfⁿ⁺¹ if Mⁿ⁺²₁ satisfies the null energy condition.