Vanishing properties of p-harmonic ℓ-forms on Riemannian manifolds

2017/04/17 by Nguyen Thac Dung, Dung, Nguyen Thac, Pham Trong Tien +1
Mathematics · #53C21 #53C24 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #msc:53C21 #msc:53C24

paper · pdf · doi:10.48550/arxiv.1704.04925

21 pages. Comments are welcome. This is a version of our paper subbmited to a journal, last February, 2016

arxiv created 2017/04/17 · openalex publication_date 2017/04/17 · arxiv updated 2017/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show several vanishing type theorems for p-harmonic ℓ-forms on Riemannian manifolds (p≥2). First of all, we consider complete non-compact immersed submanifolds Mⁿ of N^n+m with flat normal bundle, we prove that any p-harmonic ℓ-forms on M is trivial if N has pure curvature tensor and M satisfies some geometric condition. Then, we obtain a vanishing theorem on Riemannian manifolds with weighted Poincaré inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ℓ-form on M provided that Ric has suitable bound.

Citations

• Local and global sharp gradient estimates for weighted p-harmonic functions

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