Maximal subextensions of plurisubharmonic functions
Abstract
In this paper we are concerned with the problem of local and global subextensions of (quasi-)plurisubharmonic functions from a "regular" subdomain of a compact K\"ahler manifold. We prove that a precise bound on the complex Monge-Amp\`ere mass of the given function implies the existence of a subextension to a bigger regular subdomain or to the whole compact manifold. In some cases we show that the maximal subextension has a well defined complex Monge-Amp\`ere measure and obtain precise estimates on this measure. Finally we give an example of a plurisubharmonic function with a well defined Monge-Amp\`ere measure and the right bound on its Monge-Amp\`ere mass on the unit ball in for which the maximal subextension to the complex projective space does not have a globally well defined complex Monge-Amp\`ere measure.
Cite
@article{arxiv.1009.4605,
title = {Maximal subextensions of plurisubharmonic functions},
author = {U. Cegrell and S. Kołodziej and A. Zeriahi},
journal= {arXiv preprint arXiv:1009.4605},
year = {2016}
}