Mathematische Annalen

, Volume 356, Issue 4, pp 1425–1454

Stability of Kähler-Ricci flow on a Fano manifold


DOI: 10.1007/s00208-012-0889-7

Cite this article as:
Zhu, X. Math. Ann. (2013) 356: 1425. doi:10.1007/s00208-012-0889-7


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.

Mathematics Subject Classification (1991)

Primary 53C25; Secondary 53C55 58E11 

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsPeking UniversityBeijingChina

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