Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

Disc functionals and Siciak–Zaharyuta extremal functions on singular varieties

Tom 106 / 2012

Annales Polonici Mathematici 106 (2012), 171-191 MSC: Primary 32U05; Secondary 32U35. DOI: 10.4064/ap106-0-13

Streszczenie

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.

Autorzy

• Barbara Drinovec DrnovšekFaculty of Mathematics and Physics
University of Ljubljana
Institute of Mathematics, Physics and Mechanics
e-mail
• Franc ForstneričFaculty of Mathematics and Physics
University of Ljubljana
Institute of Mathematics, Physics and Mechanics