Polynomial Hulls of Arcs and Curves
| Autor: | Alexander J. Izzo |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Polynomial
Mathematics - Complex Variables Applied Mathematics General Mathematics Jordan curve theorem Functional Analysis (math.FA) 32E20 Mathematics - Functional Analysis Arc (geometry) Combinatorics Cantor set symbols.namesake Hull symbols FOS: Mathematics Complex Variables (math.CV) Mathematics |
| DOI: | 10.48550/arxiv.1912.10359 |
| Popis: | It is shown that there exist arcs and simple closed curves in C 3 \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 C N \mathbb {C}^N ( N ≥ 2 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. |
| Databáze: | OpenAIRE |
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