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Continuity of the relative extremal function on analytic varieties in ℂⁿ

100%

Wikström F.

Annales Polonici Mathematici

2005

tom 86

nr 3

219-225

Let V be an analytic variety in a domain Ω ⊂ ℂⁿ and let K ⊂ ⊂ V be a closed subset. By studying Jensen measures for certain classes of plurisubharmonic functions on V, we prove that the relative extremal function $ω_K$ is continuous on V if Ω is hyperconvex and K is regular.

Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function

51%

Carlehed M., Cegrell U., Wikström F.

Annales Polonici Mathematici

1999

tom 71

nr 1

87-103

We characterise hyperconvexity in terms of Jensen measures with barycentre at a boundary point. We also give an explicit formula for the pluricomplex Green function in the Hartogs triangle. Finally, we study the behaviour of the pluricomplex Green function g(z,w) as the pole w tends to a boundary point.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Wikström F.

1 Carlehed M.

1 Cegrell U.

1 2005

1 1999

Wyniki wyszukiwania

Continuity of the relative extremal function on analytic varieties in ℂⁿ

Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function