Stability of the Calabi flow near an extremal metric
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 1, p. 167-175

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.

Published online : 2018-06-21
Classification:  53C44,  32Q15,  32Q26
@article{ASNSP_2012_5_11_1_167_0,
     author = {Huang, Hongnian and Zheng, Kai},
     title = {Stability of the Calabi flow near an extremal metric},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {1},
     year = {2012},
     pages = {167-175},
     zbl = {1246.53088},
     mrnumber = {2953047},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2012_5_11_1_167_0}
}
Huang, Hongnian; Zheng, Kai. Stability of the Calabi flow near an extremal metric. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 1, pp. 167-175. http://www.numdam.org/item/ASNSP_2012_5_11_1_167_0/

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