L2 harmonic 2-forms on minimal hypersurfaces in spheres☆

Abstract We show that a complete noncompact minimal hypersurface M in S n + 1 ( n ≥ 3 ) admits no nontrivial L 2 harmonic 2-form if the total curvature is bounded above by a constant depending only on the dimension of M . It implies that the second space of reduced L 2 cohomology of M is trivial. This result is a generalized version of the result of Gan and Zhu on L 2 harmonic 1-forms.