Convexity of sublevel sets of plurisubharmonic extremal functions
Finnur Lárusson ; Patrice Lassere ; Ragnar Sigurdsson
Annales Polonici Mathematici, Tome 69 (1998), p. 267-273 / Harvested from The Polish Digital Mathematics Library
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Let X be a convex domain in ℂⁿ and let E be a convex subset of X. The relative extremal function uE,X for E in X is the supremum of the class of plurisubharmonic functions v ≤ 0 on X with v ≤ -1 on E. We show that if E is either open or compact, then the sublevel sets of uE,X are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:270205 
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Finnur Lárusson; Patrice Lassere; Ragnar Sigurdsson. Convexity of sublevel sets of plurisubharmonic extremal functions. Annales Polonici Mathematici, Tome 69 (1998) pp. 267-273. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv68z3p267bwm/

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