We prove that on a Kähler manifold admitting an extremal metric and for any Kähler potential close to , the Calabi flow starting at exists for all time and the modified Calabi flow starting at will always be close to . 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 exponentially fast.
@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}, pages = {167--175}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {1}, year = {2012}, mrnumber = {2953047}, zbl = {1246.53088}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_1_167_0/} }
TY - JOUR AU - Huang, Hongnian AU - Zheng, Kai TI - Stability of the Calabi flow near an extremal metric JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 167 EP - 175 VL - 11 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_1_167_0/ LA - en ID - ASNSP_2012_5_11_1_167_0 ER -
%0 Journal Article %A Huang, Hongnian %A Zheng, Kai %T Stability of the Calabi flow near an extremal metric %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 167-175 %V 11 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_1_167_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2012_5_11_1_167_0/
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