A sphere theorem for three dimensional manifolds with integral pinched curvature

In [3], we proved a number of optimal rigidity results for Riemannian manifolds of dimension greater than four whose curvature satisfies an integral pinching. In this article, we use the same integral Bochner technique to extend the results in dimension three. Then, by using the classification of closed three-manifolds with non-negative scalar curvature and a few topological considerations, we deduce optimal sphere theorems for three-dimensional manifolds with integral pinched curvature.