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Convexity of sublevel sets of plurisubharmonic extremal functions

1998; Polish Academy of Sciences; Volume: 68; Issue: 3 Linguagem: Inglês

10.4064/ap-68-3-267-273

1730-6272

Finnur Lárusson, Patrice Lassère, Ragnar Sigurðsson,

Meromorphic and Entire Functions

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