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
收藏
页码：199 / 207
页数：9
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