Vanishing theorems for L2 harmonic p-forms on Riemannian manifolds with a weighted p-Poincare inequality

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:490

Article

Zhou, Jiuru¹ 

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China

关键词: L-2 harmonic forms;    Weighted p-Poincare inequality;    p spectrum;   

DOI  :  10.1016/j.jmaa.2020.124229

来源: Elsevier

【 摘 要 】

This paper mainly deals with several vanishing results for L-2 harmonic p-forms on complete Riemannian manifolds with a weighted p-Poincare inequality and some lower bound of the curvature. Some results are in the spirit of Li-Wang, Lam, and Dung-Sung, but without assumptions of sign and growth rate of the weight function as Vieira did for manifolds with weighted Poincare inequality, and some are vanishing results without curvature restrictions. Moreover, a vanishing and splitting theorem is established with a much weaker curvature condition and a lower bound of the first eigenvalue of the Laplacian. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free