Extension of plurisubharmonic functions with growth control

Dan Coman, Vincent Guedj, Ahmed Zeriahi

Abstract: Suppose that X is an analytic subvariety of a Stein manifold M and that φ is a plurisubharmonic (psh) function on X which is dominated by a continuous psh exhaustion function u of M. Given any number c > 1, we show that φ admits a psh extension to M which is dominated by cu+ on M. We use this result to prove that any ω-psh function on a subvariety of the complex projective space is the restriction of a global ω-psh function, where ω is the Fubini–Study Kähler form.

Journal: J. Reine Angew. Math. 676 (2013), 33–49

DOI: 10.1515/CRELLE.2011.185