Extension of plurisubharmonic functions with growth control

Abstract

Suppose that $X$ is an analytic subvariety of a Stein manifold $M$ and that $\phi$ 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 $\phi$ admits a psh extension to $M$ which is dominated by $cu$ on $M$. We use this result to prove that any $\omega$-psh function on a subvariety of the complex projective space is the restriction of a global $\omega$-psh function, where $\omega$ is the Fubini-Study Kähler form.

14 pages

References in corpus (2)

• Singular Kahler-Einstein metrics
• Stability of Bounded Solutions for Degenerate Complex Monge-Ampère equations