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On the Bergman metric on bounded pseudoconvex domains an approach without the Neumann operator
https://doi.org/10.1142/S0129167X14500256Cited by:2 (Source: Crossref)
Abstract
Let 0 < ε ≤ ½ be fixed. We prove that on a bounded pseudoconvex domain D ⋐ ℂn the Bergman metric grows at least like 
times the euclidean metric, provided that on D there exists a family (φδ)δ of smooth plurisubharmonic functions with a self-bounded complex gradient (uniformly in δ), such that for any δ the Levi form of φδ has eigenvalues ≥ δ-2ε on the set {z ∈ D | δD(z) < δ}. Here, δD denotes the boundary-distance function on D.
AMSC: 32F45, 32U35
