Polynomial Hulls of Arcs and Curves

Alexander J. Izzo

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arXiv · 1912.10359

Polynomial Hulls of Arcs and Curves

Alexander J. Izzo

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Abstract

It is shown that there exist arcs and simple closed curves in ${\mathbb C}^3$ with nontrivial polynomial hulls that contain no analytic discs. It is also shown that in any bounded Runge domain of holomorphy in ${\mathbb C}^N$ ($N \geq 2$) 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.

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Alexander J. Izzo. 2019-12-21. Polynomial Hulls of Arcs and Curves. https://arxiv.org/abs/1912.10359

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