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

Abstract

This paper mainly deals with several vanishing results for L2 harmonic p-forms on complete Riemannian manifolds with a weighted p-Poincaré 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 Poincaré 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.