Abstract
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.
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