Lp harmonic 1-forms on minimal hypersurfaces with finite index

Let N be a complete simply connected Riemannian manifold with sectional curvature KN satisfying −k2≤KN≤0 for a nonzero constant k. In this paper we prove that if M is an n(≥3)-dimensional complete minimal hypersurface with finite index in N, then the space of Lp harmonic 1-forms on M must be finite dimensional for certain p>0 provided the bottom of the spectrum of the Laplace operator is sufficiently large. In particular, M has finitely many ends. These results can be regarded as an extension of Li-Wang (2002).