A Survey on the \(L^2\) Extension Theorems

Abstract

Results on the extension of \(L^2\) holomorphic functions will be described after a history of the \(L^2\) method. Applications to plurisubharmonic functions and questions in complex geometry will also be reviewed with an emphasis on the Bergman kernel.

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Correspondence to Takeo Ohsawa.

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The author expresses his deep gratitude to M. Jarnicki and P. Pflug for giving him an opportunity of writing this survey. He also thanks to S. Fu for recommending to read [60] in July 2003 in Nagoya. Last but not least, he thanks to the referee for useful suggestions.

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Ohsawa, T. A Survey on the \(L^2\) Extension Theorems. J Geom Anal 30, 1366–1395 (2020). https://doi.org/10.1007/s12220-019-00349-2

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Keywords

  • \(L^2\) holomorphic function
  • Bergman kernel
  • Plurisubharmonic function

Mathematics Subject Classification

  • Primary 32E40
  • Secondary 32T05