\(L^{2p}_f\)-harmonic 1-forms on \(f\)-minimal hypersurfaces in a weighted manifold (Q1999135)

From the paper: ``We extend the classical vanishing results of \(L^{2p}_f\)-harmonic 1-forms on a complete noncompact \(f\)-minimal hypersurface in a weighted manifold. Furthermore, we prove that there is no nontrivial \(L^{2p}_f\)-harmonic 1-forms on a complete noncompact \(f\)-minimal hypersurface in a weighted manifold under the assumption that \(M^n\) has a sufficiently small weighed \(L^n\)-norm of the second fundamental form on \(M^n\). Our results can be viewed as an extension of Yun and Seo's results given in [\textit{G. Yun} and \textit{K. Seo}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 180, 264--283 (2019; Zbl 1414.53056)].''