Estimates for the Bergman kernel and metric of convex domains in ℂⁿ
Nikolai Nikolov, Peter Pflug (2003)
Annales Polonici Mathematici
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Sharp geometrical lower and upper estimates are obtained for the Bergman kernel on the diagonal of a convex domain D ⊂ ℂⁿ which does not contain complex lines. It is also proved that the ratio of the Bergman and Carathéodory metrics of D does not exceed a constant depending only on n.