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