Asymptotic behavior of the curvature of the Bergman metric of the thin domains
This paper presents a method that studies the boundary behavior of the Riemann sectional curvature tensor of the Bergman metric of pseudoconvex domains which are a `small and thin' intersection of finitely many strongly pseudoconvex domains. The main result, roughly speaking, is that the limit of the Riemann sectional curvature tensor of the Bergman metric of such domains is that of a Siegel domain evaluated at a specific point, where the Siegel domain and the point are determined explicitly by the (piecewise smooth) local defining function of the domain near the boundary point in consideration and by the manner the point sequences approaches the boundary point in question from the interior of the original domain. The paper treats only the case of such `thin\(>\) domains. But the method in it is also applicable to a broader class containing certain weakly pseudoconvex domains.
scientific article; zbMATH DE number 4192113