书目名称 | Vitushkin’s Conjecture for Removable Sets |
编辑 | James J. Dudziak |
视频video | http://file.papertrans.cn/984/983980/983980.mp4 |
概述 | Presents a complete proof of a major recent accomplishment of modern complex analysis, the affirmative resolution of Vitushkin‘s conjecture.Includes Melnikov and Verdera‘s proof of Denjoy‘s conjecture |
丛书名称 | Universitext |
图书封面 |  |
描述 | .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 arc length measure. Chapters 6-8 of this carefully written text present a major recent accomplishment of modern complex analysis, the affirmative resolution of this conjecture. Four of the five mathematicians whose work solved Vitushkin‘s conjecture have won the prestigious Salem Prize in analysis.. Chapters 1-5 of this book provide important background material on removability, analytic capacity, Hausdorff measure, arc length 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. Although standard notation is used throughout, there is a symbol glossary at the back of the book for the reader‘s convenience.. This text can be used for a topics course or se |
出版日期 | Book 2010 |
关键词 | Analytic capacity; Arclength measure; Argument principle; Complex analysis; Garabedian duality; Hausdorff |
版次 | 1 |
doi | https://doi.org/10.1007/978-1-4419-6709-1 |
isbn_softcover | 978-1-4419-6708-4 |
isbn_ebook | 978-1-4419-6709-1Series ISSN 0172-5939 Series E-ISSN 2191-6675 |
issn_series | 0172-5939 |
copyright | Springer Science+Business Media, LLC 2010 |