Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 490, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2020.124229
Keywords
L-2 harmonic forms; Weighted p-Poincare inequality; p spectrum
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Funding
- PRC grant [NSFC 11771377]
- Natural Science Foundation of Jiangsu Province [BK20191435]
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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.
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