2010/07/01 by Dan Coman, Coman, Dan, Vincent Guedj +4 · 1 citation
Mathematics · #32Q15 #32Q28 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #Primary 32U05 #Secondary: 32C25 #math.CV #msc:32C25 #msc:32Q15 #msc:32Q28 #msc:32U05
paper · pdf · doi:10.48550/arxiv.1007.0262
14 pages
arxiv created 2010/07/01 · openalex publication_date 2010/07/01 · arxiv updated 2010/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.