Polynomial Hulls of Arcs and Curves

2019/12/21 by Alexander J. Izzo, Izzo, Alexander J.
Mathematics · #32E20 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1912.10359

openalex publication_date 2019/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that there exist arcs and simple closed curves in \mathbb C³ with nontrivial polynomial hulls that contain no analytic discs. It is also shown that in any bounded Runge domain of holomorphy in \mathbb C^N (N ≥ 2) there exist polynomially convex arcs and simple closed curves of almost full measure. These results, which strengthen earlier results of the author, are obtained as consequences of a general result about polynomial hulls of arcs and simple closed curves through Cantor sets.

Related

• Polynomially Convex Arcs in Polynomially Convex Simple Closed Curves
• Spaces with polynomial hulls that contain no analytic discs
• Polynomial Hulls of Arcs and Curves II
• The convergence of hulls of curves
• Polynomially convex sets whose union has nontrivial hull