Finnur Larusson and Evgeny A. Poletsky
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.
Journal: Michigan Math. J. 62 (2013), no. 3, 551-565.
DOI: 10.1307/mmj/1378757888