Quantitative estimates for the Green function and an application to the Bergman metric

DOI10.5802/aif.1790zbMath0960.32022OpenAlexW2021121576MaRDI QIDQ1572650

Klas Diederich, Gregor Herbort

Publication date: 19 July 2000

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2000__50_4_1205_0

zbMATH Keywords

Monge-Ampère equationBergman metricpluricomplex Green functionorder of pseudoconvex extendability

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Finite-type domains (32T25) Geometric and analytic invariants on weakly pseudoconvex boundaries (32T27) Plurisubharmonic extremal functions, pluricomplex Green functions (32U35)

Related Items (7)

On the completeness of a metric related to the Bergman metric ⋮ A note on L2-boundary integrals of the Bergman kernel ⋮ The Bergman metric and the pluricomplex Green function ⋮ On the Bergman distance on model domains in $\mathbb C^n$ ⋮ Pluripotential theory on Teichmüller space I: Pluricomplex Green function ⋮ Localization lemmas for the Bergman metric at plurisubharmonic peak points ⋮ Quasiplurisubharmonic Green functions

Cites Work

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• An estimate for the Bergman distance on pseudoconvex domains
• THE PLURICOMPLEX GREEN FUNCTION ON PSEUDOCONVEX DOMAINS WITH A SMOOTH BOUNDARY
• Extremal plurisubharmonic functions and invariant pseudodistances
• Boundary Behavior of the Caratheodory and Kobayashi Metrics on Strongly Pseudoconvex Domains in C n with Smooth Boundary
• Hyperconvexity and Bergman completeness
• Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function

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