Extension of plurisubharmonic functions with growth control
Dan Coman, Vincent Guedj, Ahmed Zeriahi

TL;DR
This paper proves that plurisubharmonic functions on subvarieties of Stein manifolds can be extended to the whole manifold with controlled growth, and applies this to functions on projective space, enhancing understanding of psh extension properties.
Contribution
It establishes a growth-controlled extension method for psh functions from subvarieties to Stein manifolds and applies this to projective space, broadening extension theory.
Findings
Extension of psh functions with growth control on Stein manifolds.
Any ω-psh function on a subvariety of projective space is a restriction of a global ω-psh function.
Abstract
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 , we show that 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 K\"ahler form.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Holomorphic and Operator Theory
