Polynomial Hulls of Arcs and Curves II

TL;DR

This paper proves that for a compact set within an arc in complex space, the polynomial hull can be described as the union of the arc and the hull of the set, refining previous results and fixing earlier inaccuracies.

Contribution

It strengthens earlier results by showing the polynomial hull of a set in an arc can be explicitly characterized, and corrects previous inaccuracies and gaps in the proof.

Findings

Polynomial hull of a set in an arc can be explicitly described.

Corrected and filled gaps in earlier proofs.

Strengthened understanding of polynomial hulls in complex analysis.

Abstract

We prove that if a compact set E in complex Euclidean space is contained in an arc J, then there is a choice of J whose polynomial hull is the union of J and the polynomial hull of E. This strengthens an earlier result of the author. We also correct an inaccuracy in the statement, and fill a gap in the proof, of that earlier result.