RICCI LOWER BOUND FOR KÄHLER–RICCI FLOW

Ricci Lower Bound for Kähler–ricci Flow

Lower bound of Ricci flow’s existence time

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. Cabeza...

A Lower Bound for the Scalar Curvature of the Standard Solution of the Ricci Flow

In this paper we will give a rigorous proof of the lower bound for the scalar curvature of the standard solution of the Ricci flow conjectured by G. Perelman. We will prove that the scalar curvature R of the standard solution satisfies R(x, t) ≥ C0/(1−t) ∀x ∈ R , 0 ≤ t < 1, for some constant C0 > 0. Recently there is a lot of study of Ricci flow on manifolds by R. Hamilton [H1-6], S.Y. Hsu [Hs1...

Local Curvature Bound in Ricci Flow

Theorem 2 Given n and v0 > 0, there exists ǫ0 > 0 depending only on n and v0 which has the following property. For any r0 > 0 and ǫ ∈ (0, ǫ0] suppose (Mn, g(t)) is a complete smooth solution to the Ricci flow on [0, (ǫr0) 2] with bounded sectional curvature, and assume that at t = 0 for some x0 ∈ M we have curvature bound |Rm |(x, 0) ≤ r 0 for all x ∈ Bg(0)(x0, r0), and volume lower bound Volg(...

A New Lower Bound for Flexible Flow Shop Problem with Unrelated Parallel Machines

Flexible flow shop scheduling problem (FFS) with unrelated parallel machines contains sequencing in flow shop where, at any stage, there exists one or more processors. The objective consists of minimizing the maximum completion time. Because of NP-completeness of FFS problem, it is necessary to use heuristics method to address problems of moderate to large scale problem. Therefore, for assessme...