Disc functionals and Siciak–Zaharyuta extremal functions on singular varieties
Volume 106 / 2012
Annales Polonici Mathematici 106 (2012), 171-191
MSC: Primary 32U05; Secondary 32U35.
DOI: 10.4064/ap106-0-13
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 $\mathbb C^n$ by Lempert and by Lárusson and Sigurdsson.
