Some
Applications of the
Ohsawa-Takegoshi Extension Theorem
Professor Zbigniew Błocki
Abstract
The extension theorem, proved by Takeo Ohsawa and Kensho Takegoshi in 1986, says that for any bounded pseudoconvex domain D
and a hyperplane H
in Cn every L2
holomorphic function in D Ç H
can be extended to an L2 holomorphic
function in D, with the estimate for
the L2-norms depending only on the
diameter of D. Moreover, the L2-norms may be taken with respect
to an arbitrary plurisubharmonic weight. This result,
together with its various generalizations, turned out to be one of the most
important and useful in Several Complex Variables in the last 20 years. We will
present several applications of the extension theorem: estimates for the
Bergman kernel, the Suita conjecture, Demailly's
regularization of plurisubharmonic functions, a
simple proof of the Siu theorem on analyticity of
sublevel sets of Lelong numbers for plurisubharmonic functions (due to Demailly).
Date: |
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Time: |
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Place: |
Room 517, Meng Wah Complex, HKU |
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All are
welcome |
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