Vitushkin<U+0019>s Conjecture for Removable Sets

• Main Author: Dudziak, James J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2010.
• Series: Universitext,
• Subjects: Mathematics.; Differential equations, partial.; Several Complex Variables and Analytic Spaces.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4419-6709-1

Vitushkin's conjecture, a special case of Painlev'̌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...

Table of Contents:

• Preface
• 1 Removable Sets and Analytic Capacity
• 2 Removable Sets and Hausdorff Measure
• 3 Garabedian Duality for Hole-Punch Domains
• 4 Melnikov and Verdera's Solution to the Denjoy Conjecture
• 5 Some Measure Theory
• 6 A Solution to Vitushkin's Conjecture Modulo Two Difficult Results
• 7 The T(b) Theorem of Nazarov, Treil, and Volberg
• 8 The Curvature Theorem of David and Lǧer
• Postscript: Tolsa's Theorem
• Bibliography
• Symbol Glossary & List
• Index.