Bounding sectional curvature along a Kähler-Ricci flow

Ruan, Wei-Dong; Zhang, Yuguang; Zhang, Zhenlei

Bounding sectional curvature along a Kähler-Ricci flow

Authors

Ruan, Wei-Dong

Zhang, Yuguang

Zhang, Zhenlei

Description

If a normalized Kähler-Ricci flow $g(t),t\in[0,\infty),$ on a compact Kähler $n$-manifold, $n\geq 3$, of positive first Chern class satisfies $g(t)\in 2πc_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the curvature operator will also uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a Kähler-Ricci soliton.