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Russian-Chinese ņonference on complex analysis and complex geometry
April 16, 2026 11:20, Moscow, Steklov Mathematical Institute, Conference Hall, 9-th floor


Non-extendability of complex structures

Zizhou Tang

Nankai University



Abstract: There exists a complex structure $J$ on a connected open subset $N$ of $S^6$. We prove that: (1) $J$ can be extended to a global almost complex structure $J_1$ on $S^6$; (2) any extension to $S^6$ is necessarily non-integrable. Therefore, it is impossible to deform $J_1$ to an integrable almost complex structure on $S^6$ while fixing it on $N$. This phenomenon indicates that the deformation strategy suggested by S.-T. Yau in his Problem 52 cannot be realized in this sense.

Language: English

Website: https://mian.ktalk.ru/jof8kvar8ayv?pinCode=5625


© Steklov Math. Inst. of RAS, 2026