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Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 195–217 | Cite as

L p harmonic 1-form on submanifold with weighted Poincaré inequality

  • Xiaoli Chao
  • Yusha Lv
Article
  • 52 Downloads

Abstract

We deal with complete submanifolds with weighted Poincaré inequality. By assuming the submanifold is δ-stable or has sufficiently small total curvature, we establish two vanishing theorems for L p harmonic 1-forms, which are extensions of the results of Dung-Seo and Cavalcante-Mirandola-Vitório.

Keywords

weighted Poincaré inequality δ-stability Lpharmonic 1-form property (Pϱ

MSC 2010

53C42 53C50 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.School of Mathematics, Southeast UniversityJiangsuP. R. China
  2. 2.School of Mathematics, Wuhan UniversityHubeiP. R. China

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