Suita conjecture and the Ohsawa-Takegoshi extension theorem

We prove a conjecture of N. Suita which says that for any bounded domain D in ℂ one has , where c D ( z ) is the logarithmic capacity of ℂ∖ D with respect to z ∈ D and K D the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.

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Bibliographische Detailangaben
Veröffentlicht in:	Inventiones mathematicae 2013-07, Vol.193 (1), p.149-158
1. Verfasser:	Bocki, Zbigniew
Format:	Artikel
Sprache:	eng
Schlagworte:	Kernels Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We prove a conjecture of N. Suita which says that for any bounded domain D in ℂ one has , where c D ( z ) is the logarithmic capacity of ℂ∖ D with respect to z ∈ D and K D the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.
ISSN:	0020-9910 1432-1297
DOI:	10.1007/s00222-012-0423-2