Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties

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.

Lemma 2.3 and new examples added; to appear in Ann. Polon. Math

References in corpus (1)

• The Poletsky-Rosay theorem on singular complex spaces

Cited by in corpus (7)

• The Poletsky-Rosay theorem on singular complex spaces
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• A note on weighted homogeneous Siciak-Zaharyuta extremal functions
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• Gluing techniques and envelopes of disc functionals on almost complex manifolds
• Lelong functional on almost complex manifolds
• A disc formula for plurisubharmonic subextensions in manifolds