Plurisubharmonic subextensions as envelopes of disc functionals

Details Plurisubharmonic subextensions as envelopes of disc functionals Plurisubharmonic subextensions as envelopes of disc functionals

2012-01-27

arxiv.org/abs/1201.5875v2

Mathematics

Complex Variables

Version 2: Erroneous example removed and a few minor changes made

Scientific paper

We prove a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain $W$ in a Stein manifold to a larger domain $X$ under suitable conditions on $W$ and $X$. We introduce a related equivalence relation on the space of analytic discs in $X$ with boundary in $W$. The quotient, if it is Hausdorff, is a complex manifold with a local biholomorphism to $X$. We use our disc formula to generalise Kiselman's minimum principle. We show that his infimum function is an example of a plurisubharmonic subextension.

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