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arXiv · 2304.09710

Complete $\lambda$-submanifolds in Gauss spaces

Doan The Hieu
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Abstract

In this paper, we study $\lambda$-submanifolds of arbitrary codimensions in Gauss spaces. These submanifolds can be seen as natural generalizations of self-shrinker and $\lambda$-hypersurfaces. Using a divergence type theorem and some Simons' type identities, we prove some halfspace type theorems and gap theorems for complete proper $\lambda$-submanifolds. These generalized our as well as the others' results for self-shrinker or $\lambda$-hypersurfaces to $\lambda$-submanifolds.

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Doan The Hieu. 2023-04-19. Complete $\lambda$-submanifolds in Gauss spaces. https://arxiv.org/abs/2304.09710

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