Guest lecture on

Several Complex Variables

Some Applications of the

Ohsawa-Takegoshi Extension Theorem

Professor Zbigniew Błocki

Jagiellonian University, Kraków, Poland

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:	May 2, 2007 (Wednesday)
Time:	3:00 – 5:45pm
Place:	Room 517, Meng Wah Complex, HKU

All are welcome