Einstein manifolds with finite Lp-norm of the Weyl curvature

This paper also states that W goes to zero uniformly at infinity if for p≥n2, the Lp-norm of W of M with non-positive scalar curvature and positive Yamabe constant is finite. Assume that M has negative scalar curvature and the Lα-norm of W is finite. As application, we prove that M is a hyperbolic space form if the Lp-norm of W is sufficiently small, which generalizes an Ln2-norm of W pinching theorem in [19].