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ArticleOriginal scientific text

Title

Convexity of sublevel sets of plurisubharmonic extremal functions

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada
  2. Laboratoire de Mathématiques E. Picard, Université Paul Sabatier - Toulouse, 3 118 route de Narbonne, F-31062 Toulouse Cedex, France
  3. Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavík, Iceland

Abstract

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.

Keywords

ENG
plurisubharmonic, relative extremal function, convex, disc functional, envelope, Blaschke product

Bibliography

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Annales Polonici Mathematici
1998/68/3
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Pages:
267-273
Main language of publication
English
Received
1997-05-15
Accepted
1997-09-22
Published
1998
Exact and natural sciences