Home » Nonfiction » James J Dudziak » Vitushkin’s Conjecture for Removable Sets

December 09 , 2008

Vitushkin’s Conjecture for Removable Sets


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.

How to download book

Buy this book

You can buy this book now only for $86.99. This is the lowest price for this book.

Buy book

Download book free

If you want to download this book for free, please register, approve your account and get one book for free.


After that you may download book «Vitushkin’s Conjecture for Removable Sets»:

Download Adobe DRM:


Download FB2: