Czechoslovak Mathematical Journal, first online, pp. 1-23
$L^p$ harmonic $1$-form on submanifold with weighted Poincaré inequality
Xiaoli Chao, Yusha Lv
Received August 4, 2016. First published January 19, 2018.
Abstract: 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.
Affiliations: Xiaoli Chao, School of Mathematics, Southeast University, 2 Sipailou, Xuanwu, Nanjing 211189, Jiangsu, P. R. China, e-mail: firstname.lastname@example.org, Yusha Lv, School of Mathematics, Wuhan University, Meiyuan 2nd Road, Wuhan 430072, Hubei, P. R. China, e-mail: email@example.com