A Selection Theorem for the Carathéodory Kernel Convergence of Pointed Domains
Kang‐Tae Kim, Thomas Pawlaschyk · Journal of Geometric Analysis · 2025
Abstract We present a selection theorem for domains in $$\mathbb C^n$$ C n , $$n\ge 1$$ n ≥ 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.