Geodesic
$L^p$ harmonic $1$-form on submanifold with weighted Poincaré inequality
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 195-217 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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},
     journal = {Czechoslovak Mathematical Journal},
     pages = {195--217},
     year = {2018},
     volume = {68},
     number = {1},
     doi = {10.21136/CMJ.2018.0415-16},
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     zbl = {06861575},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0415-16/}
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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

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