A Note on the Hyperconvexity of Pseudoconvex Domains Beyond Lipschitz Regularity

A Note on the Hyperconvexity of Pseudoconvex Domains Beyond Lipschitz Regularity

We show that bounded pseudoconvex domains that are Hölder continuous for all α < 1 are hyperconvex, extending the well-known result by Demailly (Math. Z. 194 (4) 519–564, 1987 ) beyond Lipschitz regularity.

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Veröffentlicht in:Potential analysis 2015-10, Vol.43 (3), p.531-545
Hauptverfasser: Avelin, Benny, Hed, Lisa, Persson, Håkan
Format: Artikel
Sprache:eng
Schlagworte:
Boundary regularity
Bounded exhaustion function
Continuous boundary
Functional Analysis
Geometry
Hyperconvexity
Hölder for all exponents
lder for all exponents
Log-Lipschitz
Matematik
Mathematics
Mathematics and Statistics
Plurisubharmonic functions
Potential Theory
Probability Theory and Stochastic Processes
Reinhardt domains
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Beschreibung
Zusammenfassung:We show that bounded pseudoconvex domains that are Hölder continuous for all α < 1 are hyperconvex, extending the well-known result by Demailly (Math. Z. 194 (4) 519–564, 1987 ) beyond Lipschitz regularity.
ISSN:0926-2601
1572-929X
1572-929X
DOI:10.1007/s11118-015-9486-1