We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the Siciak-Zaharyuta extremal function of an open set in a locally irreducible affine algebraic variety as the envelope of certain disc functionals, similarly to what has been done for open sets in ℂⁿ by Lempert and by Lárusson and Sigurdsson.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-13,
author = {Barbara Drinovec Drnov\v sek and Franc Forstneri\v c},
title = {Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {171-191},
zbl = {1258.32011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-13}
}
Barbara Drinovec Drnovšek; Franc Forstnerič. Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties. Annales Polonici Mathematici, Tome 105 (2012) pp. 171-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-13/