Geodesic
Stability of the Calabi flow near an extremal metric
Huang, Hongnian1 ; Zheng, Kai2
1 Centre interuniversitaire de recherches en géométrie et topologie Université du Québec à Montréal Case postale 8888, Succursale centre-ville Montréal (Québec), H3C 3P8, Canada
2 Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing, 100190, P.R. China
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 1, pp. 167-175

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We prove that on a Kähler manifold admitting an extremal metric ω and for any Kähler potential ϕ 0 close to ω, the Calabi flow starting at ϕ 0 exists for all time and the modified Calabi flow starting at ϕ 0 will always be close to ω. Furthermore, when the initial data is invariant under the maximal compact subgroup of the identity component of the reduced automorphism group, the modified Calabi flow converges to an extremal metric near ω exponentially fast.

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Classification : 53C44, 32Q15, 32Q26

Huang, Hongnian 1 ; Zheng, Kai 2

1 Centre interuniversitaire de recherches en géométrie et topologie Université du Québec à Montréal Case postale 8888, Succursale centre-ville Montréal (Québec), H3C 3P8, Canada
2 Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing, 100190, P.R. China 
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     title = {Stability of the {Calabi} flow near an extremal metric},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Huang, Hongnian; Zheng, Kai. Stability of the Calabi flow near an extremal metric. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 1, pp. 167-175. http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_1_167_0/