Lower bound of Ricci flow’s existence time

xu, guoyi;

Let (Mn, g) be a compact n-dimensional (n >= 2) manifold with nonnegative Ricci curvature, and if n >= 3, then we assume that (Mn, g) × R has nonnegative isotropic curvature. The lower bound of the Ricci flow’s existence time on (Mn, g) is proved. This provides an alternative proof for the uniform lower bound of a family of closed Ricci flows’ maximal existence times, which was first proved by E. Cabezas-Rivas and B. Wilking. We also get an interior curvature estimate for n = 3 under Rc >= 0 assumption among others. Combining these results, we proved the shorttime
existence of the Ricci flow on a large class of three-dimensional open manifolds, which admit
some suitable exhaustion covering and have nonnegative Ricci curvature.