Abstract
In this paper we will prove vanishing and finiteness theorems for L2-harmonic 1-forms on a locally conformally flat Riemannian manifold which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature is non-positive or satisfies some integral pinching conditions. Based on these vanishing and finiteness theorems, combining with the work of Li–Tam, we can obtain some one-end and finite ends theorems.
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