Equality between the Bergman metric and Carath\'{e}odory metric
Bo-Yong Chen, Yuanpu Xiong, Liyou Zhang
TL;DR
This paper establishes a precise equality between the Bergman metric and the Carathéodory metric, two fundamental concepts in complex analysis, revealing a deep connection between these geometric structures.
Contribution
It proves a new equality between the Bergman and Carathéodory metrics, which were previously studied as distinct entities in complex geometry.
Findings
Bergman metric equals Carathéodory metric under certain conditions
Provides a new understanding of metric relationships in complex analysis
Potential implications for complex geometric function theory
Abstract
We present an equality between the Bergman metric and Carath\'{e}odry metric.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Meromorphic and Entire Functions