Polynomial convexity of the closure of bounded pseudoconvex domains and its applications in dense holomorphic curves

Article Type

Research Article

Publication Title

Journal of Mathematical Analysis and Applications

Abstract

In this paper, we prove that the closure of a C2-smooth bounded strongly pseudoconvex domain is polynomially convex if it is invariant under positive time flows of a holomorphic vector field that has a globally attracting fixed point inside the domain. We also provide a sufficient condition for a bounded pseudoconvex domain so that its closure is polynomially convex. We show that if a class of bounded pseudoconvex domain Ω in Cn which are invariant under the positive time flow of certain complete holomorphic vector fields, then given any connected complex manifold Y, there exists a holomorphic map from the unit disc to the space of all holomorphic maps from Ω to Y whose image is dense in O(Ω,Y). This also yields us the existence of a O(Ω,Y)-universal map for any generalized translation on Ω, which implies the hypercyclicity of certain composition operators on O(Ω,Y).

DOI

10.1016/j.jmaa.2025.129752

Publication Date

12-1-2025

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