Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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L2 HARMONIC 1-FORMS ON SUBMANIFOLDS WITH WEIGHTED POINCARÉ INEQUALITY

  • Chao, Xiaoli (Department of Mathematics Southeast University) ;
  • Lv, Yusha (Department of Mathematics Southeast University)
  • Received : 2015.03.22
  • Published : 2016.05.01
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Abstract

In the present note, we deal with $L^2$ harmonic 1-forms on complete submanifolds with weighted $Poincar{\acute{e}}$ inequality. By supposing submanifold is stable or has sufficiently small total curvature, we establish two vanishing theorems for $L^2$ harmonic 1-forms, which are some extension of the results of Kim and Yun, Sang and Thanh, Cavalcante Mirandola and $Vit{\acute{o}}rio$.

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References

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