L2 harmonic 1-forms on minimal submanifolds in hyperbolic space

In this paper, we prove the nonexistence of L2 harmonic 1-forms on a complete super stable minimal submanifold M in hyperbolic space under the assumption that the first eigenvalue λ1(M) for the Laplace operator on M is bounded below by (2n−1)(n−1). Moreover, we provide sufficient conditions for minimal submanifolds in hyperbolic space to be super stable.