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Boundary behavior of the Bergman metric. (English) Zbl 0533.32012
Complex analysis of several variables, Proc. Symp., Madison/Wis. 1982, Proc. Symp. Pure Math. 41, 59-67 (1984).
[For the entire collection see Zbl 0527.00006.]
This paper is concerned with the Bergman metric on pseudoconvex domains. The main result is that the Bergman metric blows up at a polynomial rate if the boundary is real analytic.

MSC:
32F45 Invariant metrics and pseudodistances in several complex variables
32T99 Pseudoconvex domains
32A40 Boundary behavior of holomorphic functions of several complex variables