In this article it is shown that the Bergman metric on a bounded hyperconvex domain in C n is always complete. A counterexample demonstrates, that the converse conclusion fails in general.
Abstract. A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one smooth boundary point of finite type in the sense of D'Angelo.
We study the class of smooth bounded weakly pseudoconvex domains D ⊂ C 2 , that are of finite type (in the sense of J. Kohn) and prove effective estimates on the invariant distances of Bergman and Kobayashi and also for the inner distance that is associated to the Caratheodory distance.
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