Behavior of the Bergman kernel and metric near convex boundary points

2002/01/10 by Николай Николов, Nikolai Nikolov, Nikolov, Nikolai +2
Mathematics · #32A25 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32A25

paper · pdf · doi:10.48550/arxiv.math/0201088

arxiv created 2002/01/10 · openalex publication_date 2002/01/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The boundary behavior of the Bergman metric near a convex boundary point z₀ of a pseudoconvex domain D⊂\CCⁿ is studied; it turns out that the Bergman metric at points z∈ D in direction of a fixed vector X₀∈\CCⁿ tends to infinite, when z is approaching z₀, if and only if the boundary of D does not contain any analytic disc through z₀ in direction of X₀.

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