A Selection Theorem for the Carathéodory Kernel Convergence of Pointed Domains

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2025年6月28日

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Kang-Tae Kim,
Thomas Pawlaschyk

摘要

We present a selection theorem for domains in $\mathbb C^n$ $C^{n}$ , $n\ge 1$ $n \geq 1$ , which states that any tamed sequence of pointed connected open subsets admits a subsequence convergent to its own kernel in the sense of Carathéodory. Not only is this analogous to the well-known Blaschke selection theorem for compact convex sets, but it fits better in the study of normal families of biholomorphic maps with varying domains and ranges.