On the completeness of a metric related to the Bergman metric
Zywomir Dinew
TL;DR
This paper investigates the completeness of a metric related to the Bergman metric on bounded domains, providing a criterion for completeness and demonstrating its completeness in hyperconvex domains.
Contribution
It introduces a new criterion for the metric's completeness and proves its completeness specifically in hyperconvex domains.
Findings
The metric's completeness criterion is analogous to Kobayashi's criterion.
The metric is complete in hyperconvex domains.
Provides theoretical insights into metric completeness related to the Bergman metric.
Abstract
We study the completeness of a metric which is related to the Bergman metric of a bounded domain. We provide a criterion for its completeness in the spirit of the Kobayashi criterion for the completeness of the Bergman metric. In particular we prove that in hyperconvex domains our metric is complete.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Meromorphic and Entire Functions