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http://dx.doi.org/10.4134/JKMS.j170575

VANISHING PROPERTIES OF p-HARMONIC ℓ-FORMS ON RIEMANNIAN MANIFOLDS  

Nguyen, Thac Dung (Department of Mathematics Mechanics and Informatics College of Science Viet Nam National University)
Pham, Trong Tien (Department of Mathematics Mechanics and Informatics College of Science Viet Nam National University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.5, 2018 , pp. 1103-1129 More about this Journal
Abstract
In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.
Keywords
p-harmonic functions; flat normal bundle; locally conformally flat; weighted p-Laplacian; weighted $Poincar{\acute{e}}$ inequality;
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