$L^{2p}_{f}$-harmonic $1$-forms on $f$-minimal hypersurfaces in a weighted manifold

Abstract

In this paper, we prove the nonexistence of $L^{2p}_{f}$-harmonic $1$-forms on a complete noncompact $f$-minimal hypersurface in a weighted manifold with nonpositive sectional curvature. This results can be viewed as an extension of Yun and Seo's results on $L^{2}_{f}$-harmonic $1$-forms.