Extension of plurisubharmonic functions with growth control

Suppose that is an analytic subvariety of a Stein manifold and that is a plurisubharmonic (psh) function on which is dominated by a continuous psh exhaustion function of . Given any number  > 1, we show that φ admits a psh extension to which is dominated by on We use this result to prove that any...

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Bibliographic Details
Published in:Journal für die reine und angewandte Mathematik 2013, Vol.2013 (676), p.33-49, Article 33
Main Authors: Coman, Dan, Guedj, Vincent, Zeriahi, Ahmed
Format: Article
Language:English
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Summary:Suppose that is an analytic subvariety of a Stein manifold and that is a plurisubharmonic (psh) function on which is dominated by a continuous psh exhaustion function of . Given any number  > 1, we show that φ admits a psh extension to which is dominated by on We use this result to prove that any -psh function on a subvariety of the complex projective space is the restriction of a global -psh function, where is the Fubini–Study Kähler form.
ISSN:0075-4102
1435-5345
DOI:10.1515/CRELLE.2011.185