Polynomial hulls of arcs and curves

Izzo, Alexander

doi:10.1090/proc/15138

Polynomial hulls of arcs and curves
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by Alexander J. Izzo PDF

Proc. Amer. Math. Soc. 149 (2021), 199-207 Request permission

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, connected 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 compact, totally disconnected sets.

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