Stability on Kähler-Ricci flow, I

Abstract

In this paper, we prove that Kähler-Ricci flow converges to a Kähler-Einstein metric (or a Kähler-Ricci soliton) in the sense of Cheeger-Gromov as long as an initial Kähler metric is very closed to $g_{KE}$ (or $g_{KS}$) if a compact Kähler manifold with $c_1(M)>0$ admits a Kähler Einstein metric $g_{KE}$ (or a Kähler-Ricci soliton $g_{KS}$). The result improves Main Theorem in [TZ3] in the sense of stability of Kähler-Ricci flow.

27 pages

References in corpus (1)

• Convergence of a Kähler-Ricci flow