The Carath\'{e}odory and Kobayashi/Royden Metrics by Way of Dual Extremal Problems
Halsey Royden, Pit-Mann Wong, Steven G. Krantz
TL;DR
This paper explores the Carathéodory and Kobayashi metrics using dual extremal problems in functional analysis, providing new insights especially for convex domains.
Contribution
It introduces a novel approach to analyze these metrics through dual extremal problems, advancing understanding in convex domain contexts.
Findings
New characterization of metrics via dual extremal problems
Enhanced understanding of convex domain metrics
Potential applications in complex analysis and geometry
Abstract
We study the Carath\'{e}odory and Kobayashi metrics by way of the method of dual extremal problems in functional analysis. Particularly incisive results are obtained for convex domains.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Algebraic and Geometric Analysis