Extension of plurisubharmonic functions with growth control
By Dan Coman, Vincent Guedj, Ahmed Zeriahi. 2010
83 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0317acc010b2be3a5f167603437eaff9f1b9cde0
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In Applied Mathematics
- Valentino Tosatti
- Tristan C. Collins
- B. Weinkove
- Xiaokui Yang
- Yuguang Zhang
- G'abor Sz'ekelyhidi
- Chi Li
- Fang Zheng
In Geometry and Topology
- Valentino Tosatti
- Tristan C. Collins
- B. Weinkove
- Xiaokui Yang
- Yuguang Zhang
- G'abor Sz'ekelyhidi
- Chi Li
- Duong H. Phong
Citations in the corpus
- Kähler currents and null loci (2013, background): “The problem of extending positive currents from subvarieties has recently generated a great deal of interest in both analytic and geometric applications [16,29,42,61].”