Geodesic
$L^p$ harmonic $1$-form on submanifold with weighted Poincaré inequality
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 195-217.

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We deal with complete submanifolds with weighted Poincaré inequality. By assuming the submanifold is $\delta $-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.
DOI : 10.21136/CMJ.2018.0415-16
Classification : 53C42, 53C50
Keywords: weighted Poincaré inequality; $\delta $-stability; $L^{p}$ harmonic $1$-form; property $(\mathcal {P}_\rho )$ 
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     title = {$L^p$ harmonic $1$-form on submanifold with weighted {Poincar\'e} inequality},
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Chao, Xiaoli; Lv, Yusha. $L^p$ harmonic $1$-form on submanifold with weighted Poincaré inequality. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 195-217. doi : 10.21136/CMJ.2018.0415-16. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0415-16/

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