Vitushkin's conjecture for removable sets / by James J. Dudziak
- 作者： Dudziak, James J.
- 其他作者：
- 其他題名：
- Springer eBooks
- 出版： New York, NY : Springer Science+Business Media, LLC 2010
- 叢書名： Universitext
- 主題： Analytic sets. , Set theory. , Analytic functions. , Mathematics. , Several Complex Variables and Analytic Spaces.
- ISBN： 9781441967091 (electronic bk.) 、 9781441967084 (paper)
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電子書
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讀者標籤：
- 系統號： 005178914 | 機讀編目格式
館藏資訊
Vitushkin's conjecture, a special case of Painlevé's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arclength measure. Chapters 1-5 of the book provide important background material on removability, analytic capacity, Hausdorff measure, arclength measure, and Garabedian duality that will appeal to many analysts with interests independent of Vitushkin's conjecture. The fourth chapter contains a proof of Denjoy's conjecture that employs Melnikov curvature. A brief postscript reports on a deep theorem of Tolsa and its relevance to going beyond Vitushkin's conjecture. This text can be used for a topics course or seminar in complex analysis. To understand it, the reader should have a firm grasp of basic real and complex analysis.