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Stability of the
Kähler–Ricci flow in the space of Kähler metrics
Kai Zheng |
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Vol. 251 (2011), No. 2, 469–497
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Abstract |
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We prove that on a Fano manifold M admitting a Kähler–Ricci soliton (ω,X), if the initial Kähler metric ωφ0 is close to ω in a certain weak sense, then the weak Kähler–Ricci flow exists globally and converges in the sense of Cheeger and Gromov. In particular, φ0 is not assumed to be KX-invariant. The methods used are based on the metric geometry of the space of the Kähler metrics and are potentially applicable to other stability problems of geometric flows near the corresponding critical metrics. |
Keywords
Kähler–Ricci flow, space of Kähler metrics, stability
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Mathematical Subject Classification 2000
Primary: 32Q20, 53C25
Secondary: 53C55, 58E11
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Milestones
Received: 23 May 2010
Revised: 18 November 2010
Accepted: 23 February 2011
Published: 3 June 2011
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Authors |
| Kai Zheng | |
| Academy of Mathematics and Systems
Science Chinese Academy of Sciences Beijing, 100190 China |
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