Observational analysis shows a proper holomorphic embedding exists in bounded strictly convex domains, indicating potential applications in complex analysis.
Assume that is a bounded, strictly pseudoconvexed domain with C² boundary. Let D⊂ Cⁿ be a bounded strictly convex domain in a geometric sense, i.e. D is bounded and convex without any line segment in the boundary. If n is large enough, then there exists a proper holomorphic embedding f: → D , which extends continuously through ̄ .
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Piotr Kot (2025) studied this question.
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