POLYNOMIAL HULLS OF ARCS AND CURVES

被引：3

作者：

Izzo, Alexander J. ^{[1
]}

机构：

[1] Bowling Green State Univ, Dept Math & Stat, Bowling Green, OH 43403 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 01期

关键词：

Polynomial convexity; polynomial hull; hull without analytic structure; analytic disc; dense invertibles; arc; simple closed curve; Cantor set; Runge domain; APPROXIMATION;

D O I：

10.1090/proc/15138

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that there exist arcs and simple closed curves in 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 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 compact, totally disconnected sets.

引用

页码：199 / 207

页数：9

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