Geodesic
Vanishing properties of $f$-minimal hypersurfaces in a complete smooth metric measure space
Sbornik. Mathematics, Tome 211 (2020) no. 11, pp. 1612-1622 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $(N^{n+1},g,e^{-f}dv)$ be a complete smooth metric measure space with $M^{n}$ being a complete noncompact $f$-minimal hypersurface in $N^{n+1}$. In this paper, we extend the classical vanishing theorems for $L^2$-harmonic $1$-forms on a complete minimal hypersurface to a weighted manifold. In addition, we obtain a vanishing result under the assumption that $M^n$ has sufficiently small weighted $L^n$-norm of the second fundamental form on $M^{n}$, which can be regarded as a generalization of a result by Yun and Seo. Bibliography: 26 titles. 
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     title = {Vanishing properties of $f$-minimal hypersurfaces in a~complete smooth metric measure space},
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R. Mi. Vanishing properties of $f$-minimal hypersurfaces in a complete smooth metric measure space. Sbornik. Mathematics, Tome 211 (2020) no. 11, pp. 1612-1622. http://geodesic.mathdoc.fr/item/SM_2020_211_11_a5/

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