p-harmonic -forms on Riemannian manifolds with a weighted Poincaré inequality

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• 作者：Nguyen Thac Dung ^{dungmath@gmail.com}
• 关键词：53C24 ; 53C21
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：150
• 期：Complete
• 页码：138-150
• 全文大小：661 K
• 卷排序：150

文摘

Given a Riemannian manifold with a weighted Poincaré inequality, in this paper, we will show some vanishing type theorems for pp-harmonic ℓn>ℓ-forms on such a manifold. We also prove a vanishing result on submanifolds in Euclidean space with flat normal bundle. Our results can be considered as generalizations of the work of Lam, Li–Wang, Lin, and Vieira (see Lam (2008), Li and Wang (2001), Lin (2015), Vieira (2016)). Moreover, we also prove a vanishing and splitting type theorem for pp-harmonic functions on manifolds with Spin (9) holonomy provided a (p,p,λ)(p,p,λ)-Sobolev type inequality which can be considered as a general Poincaré inequality holds true.