Vanishing theorem and finiteness theorem for p-harmonic 1 form

2022/10/30 by Xiangzhi Cao, Cao, Xiangzhi
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.16737

openalex publication_date 2022/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we will show vanishing theorem of p harmonic 1 form on submanifold M in M whose BiRic curvature satisfying BiRic^a ≥ Φ_a(H,S) . As an corollary, we can get the corresponding theorem for p harmonic function and p harmonic map. We also investigate the finiteness problem of p harmonic 1 form on submanifold M in M whose BiRic curvature satisfying BiRic^a ≥ -k² .

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