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Rigidity of minimal submanifolds in hyperbolic space

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We prove that if an n-dimensional complete minimal submanifold M in hyperbolic space has sufficiently small total scalar curvature then M has only one end. We also prove that for such M there exist no nontrivial L 2 harmonic 1-forms on M.

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  1. Department of Mathematics, Sookmyung Women’s University, Hyochangwongil 52, Yongsan-ku, Seoul, 140-742, Korea

    Keomkyo Seo

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  1. Keomkyo Seo
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Seo, K. Rigidity of minimal submanifolds in hyperbolic space. Arch. Math. 94, 173–181 (2010). https://doi.org/10.1007/s00013-009-0096-2

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  • DOI: https://doi.org/10.1007/s00013-009-0096-2

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