Boundary continuity of complete proper holomorphic maps

TL;DR

This paper proves that no complete proper holomorphic map from the open disc to the bidisc can extend continuously to the closed disc, highlighting a boundary behavior limitation in complex analysis.

Contribution

It establishes a new boundary continuity restriction for complete proper holomorphic maps between specific complex domains.

Findings

No such map extends continuously to the boundary.

Boundary behavior constraints are critical in complex mapping theory.

Results impact understanding of holomorphic map extensions.

Abstract

We show that there is no complete proper holomorphic map from the open disc U in C to the bidisc UxU which extends continuously to the closed disc.