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We prove that for any complete three-manifold with a lower Ricci curvaturebound and a lower bound on the volume of balls of radius one, a solution to theRicci flow exists for short time. Actually our proof also yields a(non-canonical) way to flow and regularize some interior region of anon-complete initial data satisfying the aformentioned bounds.

Short-time existence of the Ricci flow on complete, non-collapsed $3$-manifolds with Ricci curvature bounded from below