Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties
Complex Variables
2014-05-22 v3
Abstract
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 C^n by Lempert and by Larusson and Sigurdsson.
Cite
@article{arxiv.1109.3947,
title = {Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties},
author = {Barbara Drinovec Drnovsek and Franc Forstneric},
journal= {arXiv preprint arXiv:1109.3947},
year = {2014}
}
Comments
Lemma 2.3 and new examples added; to appear in Ann. Polon. Math