BOUNDING SECTIONAL CURVATURE ALONG THE KAHLER-RICCI FLOW

Abstract

If a normalized Kahler-Ricci flow g(t), t is an element of [0,infinity), on a compact Kahler manifold M, dim(C) M = n >= 3, with positive first Chern class satisfies g(t) is an element of 2 pi c(1)(M) and has curvature operator uniformly bounded in L(n)-norm, the curvature operator will also be uniformly bounded along the flow. Consequently, the flow will converge along a subsequence to a Kahler-Ricci soliton.