Geodesic
Convexity of sublevel sets of plurisubharmonic extremal functions
Annales Polonici Mathematici, Tome 68 (1998) no. 3, pp. 267-273.

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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 $u_{E,X}$ 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 $u_{E,X}$ are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.
DOI : 10.4064/ap-68-3-267-273
Keywords: plurisubharmonic, relative extremal function, convex, disc functional, envelope, Blaschke product

Finnur Lárusson 1 ; Patrice Lassere 1 ; Ragnar Sigurdsson 1

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Finnur Lárusson; Patrice Lassere; Ragnar Sigurdsson. Convexity of sublevel sets of plurisubharmonic extremal functions. Annales Polonici Mathematici, Tome 68 (1998) no. 3, pp. 267-273. doi : 10.4064/ap-68-3-267-273. http://geodesic.mathdoc.fr/articles/10.4064/ap-68-3-267-273/

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