Let be a complete smooth metric measure space with being a complete noncompact -minimal hypersurface in . In this paper, we extend the classical vanishing theorems for -harmonic -forms on a complete minimal hypersurface to a weighted manifold. In addition, we obtain a vanishing result under the assumption that has sufficiently small weighted -norm of the second fundamental form on , which can be regarded as a generalization of a result by Yun and Seo.

Bibliography: 26 titles.

中文翻译：

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完全光滑度量空间中-最小超曲面的消失特性

让成为一个完整的平滑度量空间，在 中是一个完整的非紧最小超曲面。在本文中，我们将完全最小超曲面上-harmonic -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加权范数足够小的情况下获得了一个消失的结果，这可以看作是 Yun 和 Seo 的结果的推广。

参考书目：26 个标题。