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https://hdl.handle.net/2440/84447
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Type: | Journal article |
Title: | Plurisubharmonic subextensions as envelopes of disc functionals |
Author: | Larusson, F. Poletsky, E. |
Citation: | Michigan Mathematical Journal, 2013; 62(3):551-565 |
Publisher: | University of Michigan, Department of Mathematics |
Issue Date: | 2013 |
ISSN: | 0026-2285 1945-2365 |
Statement of Responsibility: | Finnur Lárusson & 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. |
Rights: | Copyright status unknown |
DOI: | 10.1307/mmj/1378757888 |
Grant ID: | http://purl.org/au-research/grants/arc/DP120104110 |
Published version: | http://dx.doi.org/10.1307/mmj/1378757888 |
Appears in Collections: | Aurora harvest 2 Mathematical Sciences publications |
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