Stability properties and gap theorem for complete f-minimal hypersurfaces |
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Authors: | Xu Cheng Detang Zhou |
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Institution: | 1. Instituto de Matemática e Estatística, Universidade Federal Fluminense, 24020-140, Niterói, RJ, Brazil
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Abstract: | In this paper, we study complete oriented f -minimal hypersurfaces properly immersed in a cylinder shrinking soliton \((\mathbb{S}^n \times \mathbb{R},\bar g,f)\).We prove that such hypersurface with L f -index one must be either \(\mathbb{S}^n \times \{ 0\}\) or \(\mathbb{S}^{n - 1} \times \mathbb{R}\), where \({S}^{n - 1}\) denotes the sphere in \(\mathbb{S}^n\) of the same radius. Also we prove a pinching theorem for them. |
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