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Vanishing properties of -minimal hypersurfaces in a complete smooth metric measure space
Sbornik: Mathematics ( IF 0.8 ) Pub Date : 2021-01-16 , DOI: 10.1070/sm9268
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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.



中文翻译:

完全光滑度量空间中-最小超曲面的消失特性

$(N^{n+1},g,e^{-f}d​​v)$成为一个完整的平滑度量空间,$M^{n}$在 中是一个完整的非紧$f$最小超曲面$N^{n+1}$。在本文中,我们将完全最小超曲面上$L^2$-harmonic -$1$形式的经典消失定理扩展到加权流形。此外,我们在假设上的第二基本形式的$M^n$加权$L^n$范数足够小的情况下获得了一个消失的结果$M^{n}$,这可以看作是 Yun 和 Seo 的结果的推广。

参考书目:26 个标题。

更新日期:2021-01-16
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