harmonic 1-forms on minimal submanifolds in hyperbolic space

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