Theoretical analysis demonstrates vanishing theorems for L2 harmonic 1-forms on complete submanifolds, indicating new geometric constraints under small curvature.
In the present note, we deal with <TEX>L²</TEX> harmonic 1-forms on complete submanifolds with weighted <TEX>Poincare</TEX> inequality. By supposing submanifold is stable or has sufficiently small total curvature, we establish two vanishing theorems for <TEX>L²</TEX> harmonic 1-forms, which are some extension of the results of Kim and Yun, Sang and Thanh, Cavalcante Mirandola and <TEX>Vitorio</TEX>.
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Chao et al. (2016) studied this question.
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