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On regularization of plurisubharmonic functions on manifolds


Authors: Zbigniew Blocki and Slawomir Kolodziej
Journal: Proc. Amer. Math. Soc. 135 (2007), 2089-2093
MSC (2000): Primary 32U05, 32Q15, 32U25
DOI: https://doi.org/10.1090/S0002-9939-07-08858-2
Published electronically: February 2, 2007
MathSciNet review: 2299485
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Abstract: We study the question of when a $ \gamma $-plurisubharmonic function on a complex manifold, where $ \gamma $ is a fixed $ (1,1)$-form, can be approximated by a decreasing sequence of smooth $ \gamma $-plurisubharmonic functions. We show in particular that it is always possible in the compact Kähler case.

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Additional Information

Zbigniew Blocki
Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Email: Zbigniew.Blocki@im.uj.edu.pl

Slawomir Kolodziej
Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Email: Slawomir.Kolodziej@im.uj.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-07-08858-2
Keywords: Plurisubharmonic functions, K\"{a}hler manifolds, Lelong numbers
Received by editor(s): March 8, 2006
Published electronically: February 2, 2007
Additional Notes: Both authors were partially supported by KBN Grant #2 P03A 03726. The second author was also supported by the Rector of the Jagiellonian University Fund
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2007 American Mathematical Society

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