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$L^{p}$ harmonic $1$ -form on submanifold with weighted Poincaré inequality

Xiaoli Chao; Yusha Lv — 2018

Czechoslovak Mathematical Journal

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.

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

$L^{p}$ harmonic $1$ -form on submanifold with weighted Poincaré inequality