Strict plurisubharmonicity of Bergman kernels on generalized annuli

Yanyan Wang

Yanyan Wang

Annales Polonici Mathematici, Tome 111 (2014), p. 237-243 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $A_{ζ} = Ω - \bar{ρ (ζ) \cdot Ω}$ be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel $K_{ζ} (z)$ of $A_{ζ}$ is plurisubharmonic provided ρ ∈ PSH(U). It is remarkable that $A_{ζ}$ is non-pseudoconvex when the dimension of $A_{ζ}$ is larger than one. For standard annuli in ℂ, we obtain an interesting formula for $\partial ² l o g K_{ζ} / \partial ζ \partial ζ ̅$ , as well as its boundary behavior.

Publié le : 2014-01-01

Zbl 1310.32006

EUDML-ID : urn:eudml:doc:280420

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     author = {Yanyan Wang},
     title = {Strict plurisubharmonicity of Bergman kernels on generalized annuli},
     journal = {Annales Polonici Mathematici},
     volume = {111},
     year = {2014},
     pages = {237-243},
     zbl = {1310.32006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-3-2}
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Yanyan Wang. Strict plurisubharmonicity of Bergman kernels on generalized annuli. Annales Polonici Mathematici, Tome 111 (2014) pp. 237-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-3-2/