Abstract
The Ricci curvature of the Bergman metric on a bounded domain D⊂Cn is strictly bounded above by n+1 and consequently log(KDn+1gB,D), where KD is the Bergman kernel for D on the diagonal and gB,D is the Riemannian volume element of the Bergman metric on D, is the potential for a Kähler metric on D known as the Kobayashi–Fuks metric. In this note we study the localization of this metric near holomorphic peak points and also show that this metric shares several properties with the Bergman metric on strongly pseudoconvex domains.
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