Lower bound of Ricci flow's existence time

Abstract

Let ( M n , g ) be a compact n-dimensional ( n ⩾ 2 ) manifold with nonnegative Ricci curvature, and if n ⩾ 3 , then we assume that ( M n , g ) × R has nonnegative isotropic curvature. The lower bound of the Ricci flow's existence time on ( M n , 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 short-time 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.