Vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds

Abstract

This paper contains some vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds with a weighted Poincaré inequality and a certain lower bound of the curvature. The results are in the spirit of Li-Wang and Lam, but without assumptions of sign and growth rate of the weight function, so they can be applied to complete stable hypersurfaces.

arXiv comment19 pages; added references; added results in section 3