Polynomially Convex Arcs in Polynomially Convex Simple Closed Curves

TL;DR

This paper proves that every polynomially convex arc can be embedded in a polynomially convex simple closed curve and explores properties of polynomial hulls of arcs and curves outside polynomially convex sets.

Contribution

It introduces new results linking polynomially convex arcs to simple closed curves and analyzes polynomial hulls in complex analysis.

Findings

Every polynomially convex arc is contained in a polynomially convex simple closed curve.

Results on polynomial hulls of arcs and curves outside polynomially convex subsets.

Insights into the structure of polynomial hulls in complex analysis.

Abstract

We prove that every polynomially convex arc is contained in a polynomially convex simple closed curve. We also establish results about polynomial hulls of arcs and curves that are locally rectifiable outside a polynomially convex subset.