Continuously non-extendable mappings between generalized complex ellipsoids of different dimensions

TL;DR

This paper demonstrates that proper holomorphic mappings between pseudoconvex domains of different dimensions can fail to extend continuously to the boundary, generalizing known phenomena from balls to more complex domains.

Contribution

It extends the understanding of boundary behavior of holomorphic mappings from balls to pseudoconvex domains of different dimensions.

Findings

Proper holomorphic mappings between pseudoconvex domains may not extend continuously to the boundary.

The phenomenon known for balls also occurs in more general pseudoconvex domains.

Boundary non-extendability is demonstrated in the context of generalized complex ellipsoids.

Abstract

There exists a proper holomorphic mapping between balls of different dimensions such that it does not extend continuously to the boundary. The aim of this paper is to show the same phenomenon occurs for pseudoconvex domains of different dimensions.