Vanishing properties of [IMG align=ABSMIDDLE alt=$ f$]tex_sm_4895_img1[/IMG]-minimal hypersurfaces in a complete smooth metric measure space

Let be a complete smooth metric measure space with being a complete noncompact -minimal hypersurface in . In this paper, we extend the classical vanishing theorems for -harmonic -forms on a complete minimal hypersurface to a weighted manifold. In addition, we obtain a vanishing result under the assumption that has sufficiently small weighted -norm of the second fundamental form on , which can be regarded as a generalization of a result by Yun and Seo. Bibliography: 26 titles.