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On the Blocki-Zwonek conjectures
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 60, no 9, 1270-1276 p.Article in journal (Refereed) Published
Abstract [en]

Let Omega be a bounded pseudoconvex domain in C-n, and let g(Omega) (z, a) be the pluricomplex Green function with pole at a in Omega. It was conjectured by Blocki and Zwonek that the function given by beta = beta(Omega),(a) : (-infinity, 0) (sic) t -> beta(t) = log (lambda(n)({z is an element of Omega g(Omega) (z, a) < t})) is convex. Here.n is the Lebesgue measure in Cn. In this note we give an affirmative answer to this conjecture when Omega is biholomorphic to the unit ball or to the polydisc in C-n, n >= 1.

Place, publisher, year, edition, pages
2015. Vol. 60, no 9, 1270-1276 p.
Keyword [en]
Bergman kernel, Bocki-Zwonek conjectures, pluricomplex Green functions
National Category
Mathematical Analysis
URN: urn:nbn:se:umu:diva-97712DOI: 10.1080/17476933.2015.1004541ISI: 000359478400007OAI: diva2:776194
Available from: 2015-01-07 Created: 2015-01-07 Last updated: 2015-09-23Bibliographically approved

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Åhag, Per
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