Weighted p-harmonic 1-forms on f-minimal hypersurfaces in smooth metric measure spaces

In this paper, we consider [Formula: see text] weighted [Formula: see text]-harmonic 1-forms on an [Formula: see text]-minimal hypersurface [Formula: see text] in a smooth metric measure space [Formula: see text]. We establish two vanishing type theorems for [Formula: see text] weighted [Formula: see text]-harmonic [Formula: see text]-forms provided that [Formula: see text] has a sufficiently small weighted [Formula: see text]-norm of the second fundamental form on [Formula: see text]. These results can be seen as a generalization of results by Yun and Seo [ 25 ] and Mi [ 18 ].