Plurisubharmonic subextensions as envelopes of disc functionals

Abstract

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.