Holomorphic maps with large images
Bo-Yong Chen, Xu Wang

TL;DR
This paper constructs holomorphic maps from pseudoconvex domains to complex Euclidean spaces with large images, introducing a new concept of universal dominability and exploring boundary behaviors like Casorati-Weierstrass and Picard points.
Contribution
It introduces a novel approach to boundary value problems in complex analysis by constructing maps with controlled growth and boundary properties, and defines the concept of universal dominability.
Findings
Existence of holomorphic maps with large boundary images
Introduction of universal dominability concept
Construction of functions with prescribed boundary behaviors
Abstract
We show that each pseudoconvex domain admits a holomorphic map to with , where is the minimum of the boundary distance and , such that every boundary point is a Casorati-Weierstrass point of . Based on this fact, we introduce a new anti-hyperbolic concept --- universal dominability. We also show that for each and each pseudoconvex domain , there is a holomorphic function on with , such that every boundary point is a Picard point of . Applications to the construction of holomorphic maps of a given domain onto some are given.
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Taxonomy
TopicsMeromorphic and Entire Functions · Holomorphic and Operator Theory · Advanced Topology and Set Theory
