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Rigidity of Complete Minimal Hypersurfaces in the Euclidean Space

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Abstract

We show that a complete minimal hypersurface M in \({\mathbb{R}^{n+1}}\) (n ≥ 3) admits no nontrivial L 2 harmonic 2-form if the total curvature is bounded above by a constant depending only on the dimension of M. This result is a generalized version of the results of Cheng etc on L 2 harmonic 1-forms.

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Authors and Affiliations

  1. School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, 213001, Jiangsu, People’s Republic of China

    Peng Zhu

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  1. Peng Zhu
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Correspondence to Peng Zhu.

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This work was partially supported by NSFC Grants 11471145, 11371309 and Qing Lan Project

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Zhu, P. Rigidity of Complete Minimal Hypersurfaces in the Euclidean Space. Results Math 71, 63–71 (2017). https://doi.org/10.1007/s00025-015-0513-8

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  • DOI: https://doi.org/10.1007/s00025-015-0513-8

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