Abstract
In this paper, we investigate Lp harmonic 1-forms on a complete noncompact orientable stable hypersurface that is immersed in a Riemannian manifold with weighted Bi-Ricci curvature bounded from below. We obtain several vanishing properties for this class of harmonic 1-forms. Our results can be considered as a generalization and improvement of previous work. Moreover, we consider immersed f-minimal hypersurfaces in a weighted Riemannian manifold and prove that if such a hypersurface is weighted stable then the space of L2 weighted harmonic 1-forms is trivial. As a consequence, any weighted stable minimal surface must have genus zero.
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