, Volume 356, Issue 4, pp 1425-1454
Date: 14 Dec 2012

Stability of Kähler-Ricci flow on a Fano manifold

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Abstract

Let \((M,J)\) be a Fano manifold which admits a Kähler-Einstein metric \(g_{KE}\) (or a Kähler-Ricci soliton \(g_{KS}\) ). Then we prove that Kähler-Ricci flow on \((M,J)\) converges to \(g_{KE}\) (or \(g_{KS}\) ) in \(C^\infty \) in the sense of Kähler potentials modulo holomorphisms transformation as long as an initial Kähler metric of flow is very closed to \(g_{KE}\) (or \(g_{KS}\) ). The result improves Main Theorem in [14] in the sense of stability of Kähler-Ricci flow.

Partially supported by NSF10990013 and NSF11271022 in China.